Search.setIndex({desctypes:{"0":"function","1":"class","2":"attribute","3":"method"},terms:{orthogon:[5,13,7,2,0],poorli:20,four:[22,25,15],"1e7j":9,"0x0138f1f0":[],totient:22,whose:26,accur:[6,19,20,22,14,23,7,8,24,9,25,1,10,26,0,17,4,18],"29e":17,illustr:[27,8,4],matlab:[],under:[22,5,28,7,26],slowest:25,digit:[6,19,20,13,22,23,7,8,25,1,10,27,17,28,4],everi:[19,22,24,25,16,17],vastli:[],"19739830969552e":9,rise:[13,2,11,0],trigonometr:[5,25,14,15,9,16,2,23],"0x019f2530":[],affect:19,primepi2:6,"0x01357730":[],"128379167095512573896159e":9,correct:[5,19,22,23,7,8,9,25,1,10,0,4],vector:[8,10,2,0,27,17,18],math:[9,22,2,0],verif:22,tricomi:0,absmax:[19,17],"434284j":9,"10j":[19,24,11,0],wronskian:16,naiv:9,direct:[5,21,22,8,24,25,10,4,26,0,11,18],second:[6,13,15,27,9,10,26,0,16,4,18],"325717j":9,dobinskisformula:6,even:[6,19,21,22,28,27,24,9,25,10,4,26,0,16,17,11],asin:[14,23],hide:[25,19],"3697207890154e":11,loggamma:[16,24,11],"2602j":16,mw_twinprim:[],calcul:[6,19,12,13,22,23,7,25,10,4,26,27,16,17,11],"7455257875808100868984496j":0,"391492658196305j":22,"82752982813540993502j":0,roundoff:8,"new":[19,17,4,18],symmetr:[27,24,13],"0x0132c070":[],told:27,"57095384420474e":24,"27e":17,"09645e":4,"27j":26,never:27,here:[20,22,23,7,24,1,10,26,4],path:7,interpret:[5,25,28,7,9,1],"0x012d6e30":[],"085042824915332562522402j":16,intead:28,hankel:[16,2],"8057117299251e":6,loos:6,precis:[1,2,0,4,5,6,7,8,9,10,11,12,13,15,16,18,19,20,21,22,23,24,25,26,27,28],quadosc:[9,14,7,16,3],permit:[19,13,25,16,26,0,10,18],ainsworth:24,studi:[24,4],fourier:[15,20,3],"0x012f6830":[],"0x013ab5f0":[],"962288353j":6,golden:[23,6,10,2],fsub:8,"25e6":19,fsum:[22,19,4,3],linearli:[16,10,4,0],txt:24,"0x01399bf0":[],unit:[28,20,22,15,7,24,0,23],highli:[27,7],plot:[5,19,20,18],describ:[19,7,4,18],would:[22,6,1,15],call:[28,6,19,20,22,15,7,8,24,9,25,1,10,11,26,0,27,17,23,4],"3326361850321887899e":24,recommend:[25,27,28,10],factorial2:11,type:[5,6,19,13,25,28,24,1,10,2,27,17,4],until:[7,1,4],"113535539412145912607826671159289j":22,"05e":[6,17],relat:[5,6,19,22,15,11,24,9,25,10,2,0,16,23,4],exce:11,gammainc:[9,26],hold:[6,19,25,23,8,1,16,4,11],must:[19,12,20,15,8,24,10,4,26,27,28,11,18],"0x013989f0":[],springer:4,"101014101401543575679639e":6,join:22,err:[12,20],restor:19,setup:28,work:[28,6,19,20,13,22,15,7,8,24,9,25,1,10,26,0,27,23,4,18],"97746326050642263725661j":16,"0x013865b0":[],erf:[9,28,11],wors:[6,7],"55065599872579097221j":6,norm:[17,8,27],root:[5,6,7,12,13,22,14,23,3,27,24,9,25,1,10,2,0,16,11],dhbailei:7,"0x0134c930":[],novic:25,"0x01358430":[],polylogarithm:[9,5,2,24],give:[6,20,13,22,23,8,24,9,25,1,16,11,26,0,27,17,4,18],"61351758081e":20,indic:[25,19,24,4,0],caution:[],fibonacci:[6,2],want:[19,1,17,18],"0x01393630":[],keep:[19,25,1,27],"157j":16,illinoi:27,end:[22,12],straightforward:[25,17],thing:[17,23,16,11],"68e":6,ordinari:[5,13,14,15,3,24,9,0,11,18],construt:[],how:[20,25,28,8,24,9,1,27,17,11],"0x0138a5f0":[],answer:[1,4],verifi:[28,13,15,27,24,9,10,0,16,23,11],wolfram:[6,23,7,24,9,4,0,11],frobeniu:17,recogn:[7,10],outsid:[22,24,4,0],earlier:[14,28,7],oscillatori:[7,3],befor:[7,10,0,17,11,18],wrong:[6,22,7,25,1,4],beauti:11,"55e":[6,17],law:8,demonstr:[10,0],handl:[7,4,0],attempt:[25,10,4],third:[19,16,26,4,13],interpol:18,"3619719871407024816e":6,exclud:19,alias:27,environ:28,enter:25,worst:[25,10],lambda:[6,19,27,20,13,22,15,7,24,9,10,11,26,0,16,23,4,18],order:[6,20,13,22,7,24,9,10,11,26,0,16,4,18],hankelh1:[],g10:24,oper:[5,19,25,23,8,1,10,2,26,17,4],acsch:21,xlim:19,"0x015165f0":[],over:[6,19,25,14,23,7,8,24,1,4],fall:[4,22,25,2,0,11],"950440066552087387515653e":13,becaus:[27,26,20],"28713710846125e":[],"43429448190317j":9,veri:[6,19,20,22,15,7,24,9,25,4,26,27,17,11,18],pascal:11,"691023585965793j":22,"2607738054097702293308689j":0,fit:8,chebyfit:[12,20,3],fix:[13,25,15,24,9,1,10,0,16,23],better:[6,14,28,7,10,27,4,18],"237220401382240876065501e":0,fadd:[22,8],comprehens:0,easier:17,"1238733442561786843557315j":15,them:[27,7,17],"22007971511612e":22,"00222938275488344j":24,thei:[28,13,22,14,15,7,24,25,10,0,27,23,11],lambert:[22,27,2],safe:[25,19,10],overestim:7,rectangl:7,"break":[7,24],promis:9,"45626803423487934264j":24,silver:10,choic:[22,7,20,18,0],regula:27,"40j":24,each:[19,12,22,14,28,7,10,4,0,27,11,18],debug:19,randmatrix:17,side:[1,26],cl2:24,mean:[4,22,15,7,9,25,10,2,17,23,11,18],"0x019765f0":[],clausen:[6,2,24],"585621643835618941044855j":16,enorm:25,"0x01396f70":[],runtest:28,"712388980384689857693965j":[],extract:28,goe:1,dhbpaper:7,"10000j":16,content:[5,19],rewrit:0,adapt:5,asympot:[],gov:[7,24],"07895435170559j":22,linear:[5,19,7,1,10,0,17],"39e":6,"01609578360403649340169406j":0,abramowitz:[9,13,16,0],ntr:24,situat:25,infin:[19,25,23,24,9,17,4],ineffici:[9,8],nth:[22,6,2],findroot:[6,19,27,23,7,24,9,10,3,16,11],"0x016a79b0":[],muller:27,"73574e":16,convent:[22,14,8,25],angl:[14,23,8],mpmath_nogmpi:28,traceback:[22,15,8,24,9,0,27,17,11],att:11,"07e":17,erfc:[9,0],unabl:4,isc:10,subtl:25,confus:[9,24,11,0],erfi:9,rand:[9,19],rang:[5,6,19,20,13,22,14,23,7,24,9,25,10,11,26,16,4],"__add__":17,"4469098397654815837307006j":16,independ:[19,18,16,0],wast:6,thereof:10,restrict:[25,19,10],unlik:[22,8,24,11,13],alreadi:[28,7,10],"06e":17,robust:[27,7,18],rel_ep:19,agre:[6,1,11],primari:24,airi:[16,2],sometim:[28,20,15,7,10,4,0,27,17,23,11],"0x01345670":[],cumul:[9,11],master:5,too:[6,25,15,7,8,24,10,4],tol:[27,19,10,4,18],similarli:9,"35j":[],"009884375038322493720314034j":21,namespac:[],tool:28,"0x01376570":[],"146045605088568607055454e":6,took:[],quasiperiod:15,vonstaudt:6,somewhat:[22,25,1,27],conserv:[7,1],technic:[25,5,24],"17706465801374033261383j":24,"59960492420134e":14,target:[25,26,4],keyword:[19,20,13,7,8,9,10,11,26,0,27,17,4],provid:[5,6,19,12,20,22,28,7,8,24,9,25,10,0,4,18],expr:[],b_j:[],zero:[11,20,13,25,7,24,19,1,10,2,0,16,17,4],matter:[25,7,1,20],"0x15250c8":[],chebyt:13,minut:28,"0x0139b1f0":[],entail:14,modern:11,raw:[],"0x012fd7b0":[],manner:19,increment:[25,7],"500j":9,seen:4,seem:7,incompat:[25,17],lbl:7,recreat:19,djeffrei:22,latter:[17,10],cope:7,"0x018ecb70":[],"5707963267949j":22,"95885418079535738828j":0,yast:28,"5707963267949e":22,simplifi:[19,7,10],thumb:20,though:[25,7,17],object:[23,19,18],unknowingli:[],monomi:26,regular:[22,23,9,25,16,0,28,11],artifact:[25,19],phase:[19,8,24],everyth:28,prematur:10,don:[25,17,23,8],doc:28,"0x013991f0":[],doe:[19,22,7,8,24,25,1,10,0,27,4],dummi:4,bracket:19,neg:[6,19,13,22,24,9,25,1,16,4,17,11],unchang:[],tetragamma:[],dot:19,radix:25,meijerg:0,abl:[25,28,7,10,4],random:[9,17,4],sage:[5,28],maxdegre:7,radiu:[20,22,16,26,0,4,18],syntax:[27,19,17,0],"6769247817778742392j":9,noninteg:[16,26,24],cospi:14,involv:[25,23,7,9,0,17,18],"41e":6,arctang:[14,8],steffensen:27,libari:14,mnorm_1:[],"0x01385d70":[],busi:25,choleski:17,"327764910194842158583189e":13,"0x013ad530":[],mascheroni:[23,24],"16966398138119450043195899746j":6,stop:[26,4],"8495559215388j":22,ceil:[25,19,8,2,11],infti:[],watson:11,"65e":6,aand:[9,0],reconstruct:6,zetazero:24,bar:[],twice:[17,16],bad:[9,19,7,27],rung:18,mnorm_f:[],pade:[20,4,3],subintegr:7,doublefactori:11,full:[28,7,10,4],result:[6,19,20,22,14,7,8,9,25,1,10,11,26,27,17,4],respons:[],fail:[22,28,7,10,0,27],bess:[16,0],"561034538142413947789221e":16,best:[19,25,7,4,18],lerr:6,hopefulli:0,differintegr:[16,26,3],wikipedia:[27,12,24,11,0],"04942396360948e":6,"0x01388bb0":[],discoveri:7,elementwis:17,simplest:10,awai:[25,1,16,24],"0x01395bb0":[],accord:19,extend:[25,6,10,4],"0x019745f0":[],xrang:4,extens:[5,6,13,25,15,28,11],"5990701173677961037199612j":15,add:[25,17,28,8,4],extent:10,toler:[27,19,10,4],"7007434154172148e":8,"0x016bac30":[],"36j":22,cot:[14,19,2,24],irregular:[7,16],ill:[20,18],howel:24,"1574325240413029954685366j":11,futil:25,uncertainti:[25,1],com:[5,6,23,7,24,9,11,0,28,4],col:17,"0x01395b70":[],"16j":22,"634292858119162417301683j":15,inher:25,"13805976125208e":11,permut:[22,6],shortcut:[23,7,11],struveh:16,diff:[6,19,20,13,22,15,3,24,9,16,4,26,0,27,23,11],mw_zeta:[],"0x013595f0":[],assum:[6,19,13,25,14,26,0],"0x0138c770":[],speak:[],code:[5,19,25,23,7,28],gamma_n:[],grave:4,fri:5,"0x0145e8f0":[],numpi:17,three:[6,12,22,24,25,4,11],been:[6,19,7,10,26,4,18],"0x018e9bf0":[],much:[6,22,28,7,25,26,4],basic:[5,6,19,13,22,14,15,7,24,9,25,1,10,11,26,27,17,4,18],"294418620024357476985535j":9,tini:[22,25,1,24],quickli:[6,22,15,10,11,18],"25j":[6,15,24,16,0,4],chug:25,life:17,acoth:21,suppress:19,sum_next:7,"593897639029319267398803e":9,page_228:9,"375e":11,exception:7,ident:[6,13,22,15,24,9,16,27,17,23,11],"0x01356430":[],tanh:[7,4,21],properti:[6,19,22,15,7,9,1,11,0,17,4],"0912451798066779j":24,counterclockwis:[22,7],euclidean:[17,8],"0x016351f0":[],unsolv:7,"31790195707456e":16,"0x0133c030":[],"44048454290863e":26,a000178:11,clausentheorem:6,pidata:24,conj:8,sever:[20,25,28,7,24,10,27,17,4],"20j":[24,0],"6846779342253e":9,"002235061547756185403349091j":9,perform:[19,12,22,7,8,25,10,26,27,17,4,18],make:[19,22,28,7,25,1,16,26,27,17,18],transpar:28,dhb:7,"0x013997f0":[],complex:[6,11,12,26,13,22,14,15,7,8,27,24,9,19,10,2,21,0,16,4,18],split:7,complet:[5,19,15,7,9,28,11],"0x01357370":[],hand:[7,1,18],"3619719871407e":[9,6],fairli:[7,10],rais:[19,22,15,25,0,27,17],"115945364792025420300208e":0,tune:7,squar:[19,22,14,7,1,10,0,17,4],bewar:9,thu:[6,13,22,14,7,9,16,26,0],hyp1f1:0,hyp1f2:0,ellipticintegr:0,wherebi:[18,13],thi:[1,0,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28],lagrang:[],quadgl:7,"95105651629515357212j":12,left:[1,26],default_color_funct:19,identifi:[9,5,10,11,0],just:[19,12,22,28,7,24,25,10,26,0,17,18],precison:26,newton:[22,27,12],psyco:28,farther:25,"__dict__":[],"1904534692378346862841089j":9,yet:19,"53e":17,"0x0139c1f0":[],easi:[25,26,13],interfer:28,conjug:[12,8,24,11],ideal:7,"15683e":16,"0x0139a1f0":[],"8930312845682213562172j":0,expon:[25,5,19,8,2],hat:[],applic:[22,27,19,11,4],"540725411970948860173735e":16,"47845029116524e":16,preserv:[25,14,23,17,4],"16223597829874e":16,lco:[],measur:[19,25,7],specif:[22,19,10,20,4],"728805278735270407053036e":[],arbitrari:[5,6,12,20,13,22,15,11,24,9,25,16,2,26,0,23,4],manual:[27,28],modulu:15,force_typ:[27,17],hung:[],pslq:[5,10],"1918250181801757416908224j":16,www:[6,22,24,9,10,0,11],odlyzko:24,old:28,deal:7,negat:[9,8],interv:[5,6,19,20,13,22,14,7,24,9,25,1,27,17,4],interp:[],maxim:[27,17],airybi:16,intern:[17,16,28,12,25],hypot:8,toctre:5,superfac:[6,11],"0x013445b0":[],total:19,hyperfac:11,"0x013ac1f0":[],subclass:7,multipli:[20,25,7,8,10,26,16,17],"0x0150d5b0":[],condit:[15,12,20,18],umn:24,sfu:[9,10,24],nonuniform:[],confluent:[2,0],"948359035324558320217678j":16,"84901771719130765656316j":16,"46944695195361e":17,convex:21,repositori:28,"3504j":0,hadamard:23,"super":[2,11],get_nod:7,chapter:19,check_cancel:0,"97272691416282e":11,slightli:[19,13,22,28,7,25,10,26,4],"22532e":4,unfortun:[10,4],produc:[19,20,25,1,10,4],mnorm:17,"float":[5,6,19,20,22,14,23,8,24,25,1,10,0,17,11],equidist:22,bound:[17,6,1,10],down:[25,8],right:[1,26],wrap:19,precomput:10,often:[19,22,14,7,24,16,4,0,11],accordingli:[25,28,7,26,20],wai:[6,19,20,13,22,23,7,24,9,4,17,11],support:[28,6,20,22,15,7,24,9,25,1,16,11,26,0,27,17,23,4],transform:[7,10,11,4,18],guess_degre:7,"25318497558335j":22,avail:[6,19,20,22,28,7,9,25,10,2,17,4],width:[25,1],anderson:27,"186339621747690j":16,fraction:[6,19,22,23,3,8,25,10,26,0,16],amazingli:6,"0x0139a0b0":[],fresnel:[9,19,7,2],lowest:6,"0x01384eb0":[],medium:[],form:[6,19,20,22,15,24,25,10,4,0,11,18],forc:[27,28,4],epsilon:[19,23,7,17,4],"0999007139290278787734903j":16,"0x0134a1f0":[],"1071073099422j":13,"1737173j":16,"00000000005e":22,"591553486811969380442171e":6,"true":[1,0,4,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27],reset:19,"5075477124212226194278700785075126e":22,coeff:12,maximum:[19,12,20,25,7,10,4],tell:1,inaccur:[22,7,24],g_n:[],cosec:[14,21],absenc:1,opensus:28,"02058050372068958069241j":13,maxterm:4,classic:24,twinprimesconst:23,cyclotom:[6,2],"467827x":[],"17920694574172j":22,diagnost:28,exist:[22,17,10,4],afterwar:[],perez:[],download:[5,28,24],quantiti:25,check:[6,19,25,15,8,24,9,1,10,28,11,18],"08e":17,floor:[25,19,8,2],when:[19,27,20,13,22,15,7,8,24,9,25,10,11,0,16,23,4],"0x016babb0":[],laguerr:[2,13],test:[5,6,25,28,1,16,26,0,18],tie:25,presum:26,"11617e":[],node:7,"663270217461022307645625j":13,intend:25,polyroot:[6,12,13,10,3,11],findmax:27,"337048736538615712436929e":16,substract:17,"0x0137db30":[],"0x013b0570":[],consid:[27,15,7,10,11],"934099289460529j":27,"15j":16,uniformli:[],"291911213325184901239155e":0,merten:[23,2,24],"16667e":[22,14,21],faster:[6,19,22,23,7,25,10,4,26,27,17,28,11,18],coulomb:[16,2],abscissa:7,sigma:9,"48478e":4,"23378441241546j":24,geometr:[22,2,4],time:[6,19,20,28,7,24,10,4,26,17,11],backward:6,"0x013392b0":[],mathrm:[],"0x0134b870":[],"9272952180016122324285125j":22,skip:[9,19,17,20],"0x0134c870":[],global:[19,21],signific:[25,6,19],"6419643823412927142424049j":16,computation:6,row:[17,4],"0x013a3630":[],depend:[20,15,7,9,10,27],recognit:[5,10],graph:19,decim:[19,20,25,23,8,1,10,4],abs_ep:19,s_method:27,rightmost:11,tracker:28,"285447104177860806j":13,"0x019f34f0":[],multivalu:[22,14],sourc:[9,25,23,28],"3619719871407032404e":6,asymptot:[6,22,28,7,24,9,16,0,27,11],feasibl:[6,10],endpoint:[19,7,9,1,26,4],octob:4,barnes_g:11,exact:[6,11,22,23,7,8,24,19,25,1,10,2,26,0,16,4,18],"97262736954392e":11,riemann:[6,23,24,16,2,26,27],"645432555362369624818525j":9,solver:[27,24,18],did:25,die:7,gui:28,"60408207642219e":11,iter:[19,12,22,7,4,26,27,17,11],googolplex:19,item:11,"742664438034657928194889j":24,quick:19,"0x013a2030":[],round:[5,6,19,22,23,8,24,25,1,0],upper:[9,15],slower:[6,7,11,4],arccosin:14,maclaurin:[21,22,23,7,24,4],htm:[9,0],run_doctest:28,cosh:[20,4,21],"0x016bd9f0":[],"06561206166091757973112783j":24,cost:[20,4],nonaltern:[],spectral:17,"16358800377071e":16,appear:[6,12,23,16,0,11],"0x01349df0":[],"0x0138fbb0":[],"14484006887480537268266j":24,current:[19,22,23,24,25,0,17,28,4],nsum:[6,19,22,23,7,24,9,11,0,3,4],"0x202f0c8":[],deriv:[6,12,22,15,7,24,16,4,26,3,27,23,11,18],gener:[1,2,0,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],coeffici:[4,6,12,20,13,22,15,24,10,2,0,16,11],satisfi:[6,20,13,22,15,8,24,9,16,0,27,17,11],normalize_whitespac:[22,24],"0x013819f0":[],slow:[19,20,22,24,25,27,17],tangent:[14,7,21],address:25,along:[6,19,20,22,14,7,24,0,11],do_someth:19,"0x01388b70":[],shift:11,oei:11,superfactori:11,"7053886880648105068343509j":0,a002109:11,"302j":24,kinkelinconst:23,extrem:[6,22,15,7,24,25,4],"0x013b35f0":[],digamma:11,"0x013570b0":[],commonli:[15,2,11],preposter:26,regardless:[27,4],extra:[19,25,28,7,26],circumv:7,tweak:27,modul:[25,28,17,2],prefer:26,"0x016c6770":[],"807708544441684513934213e":0,"218812403109304543800741e":[],bjoerk:27,instal:[5,28],"17e":17,frexp:8,prove:1,univers:11,airyai:16,prec:[19,25,28,7,8],subvers:28,handler:19,"0x013b25f0":[],bender:4,checkout:28,"0x01398770":[],afford:17,peopl:24,finit:[19,13,25,14,7,8,24,4,26,0,11],appel:[2,0],easiest:20,"3167287567024e":9,"299602851624027900335391e":16,valle:23,uniqu:[22,25],descriptor:7,can:[1,0,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,22,23,24,25,26,27,28],primecountingfunct:9,purpos:25,mw_fib:[],"603152987479187018219533j":[],nearest:[25,6,8,23],j0zero:7,literatur:15,topic:4,critic:24,"14e":6,dxi:[],simul:18,"14j":[27,24],"547394054060638j":22,alwai:[6,25,14,23,10,4],differenti:[5,6,20,13,22,23,7,24,16,11,26,0,3,4,18],subnorm:25,multipl:[19,25,23,7,8,24,16,4,27,17,11],"0x0150a670":[],"0x0138c9b0":[],write:25,pure:[7,24],tolist:17,product:[5,6,19,25,23,24,10,4,3,11],mar:5,atan:[14,23,8,18],"01144471378225e":11,max:[25,27,6,20],clone:19,"4th":11,"0x018aba70":[],mai:[1,0,4,6,7,8,9,10,11,12,13,15,16,17,18,19,20,22,23,24,25,26,27,28],fibonaccinumb:6,data:[7,17],grow:[9,22,10,20,11],"9967577965693583104609688j":14,harmon:[23,24,2,11,18],hyperu:0,corless:22,practic:[6,7,26],stdin:17,explicit:[18,17,13],"0x015fe930":[],acot:[14,10],quadrant:8,inform:[5,28,7,9,16,0,27,4],"switch":28,combin:[12,10,0,27,16,11],"2246467991473532e":[],callabl:27,algotithm:[],"92532039161405e":9,irrat:[6,10,23],atanh:21,increas:[6,19,22,14,7,24,25,1,10,0,16,4,18],odeint:[],"7037e":24,still:[7,1,0],ieee:25,dynam:[],mw_glaisher:[],group:22,monitor:19,"82e":17,window:28,"556691003883483531962095e":9,main:[19,5,28,7],"114976146679907015775102j":0,prime:[6,19,22,23,24,9,2],non:[17,10,22,7,8],"0x01549e70":[],lu_solv:17,initi:[6,22,7,24,3,27,18],workdp:19,therebi:[10,0],half:[28,6,22,15,7,24,1,16,26,23,11],now:[25,4],"0x017caef0":[],introduct:19,term:[6,19,27,20,13,22,15,7,24,9,10,11,26,0,16,23,4],name:[25,23,7,17,4],realist:[],revers:[9,10,20,11],"93e":17,linspac:[19,7],separ:[6,22,28,24,25,10,26],"52359877559829887308j":24,"143324917492256448770769e":16,updat:[19,4],compil:[25,5,28],domain:9,notabl:[19,7,4],"41567059811949e":16,replac:4,individu:[28,19,0],continu:[6,23,24,16,4,26,0,11,18],significantli:[25,6,10,23],"36938578794354e":16,operand:[25,23],happen:[22,10,24,18],shown:[6,19,10,24],accomplish:7,pentagamma:[],space:[19,4],kummer:0,barnesg:[23,11],"0x01384c30":[],"3619619242700451992411724j":11,formula:[6,19,20,13,22,15,7,24,25,10,4,26,16,23,11],factori:[5,6,22,2,0,11],gram:[6,2,24],after:[13,28,10,0,27,4],pseudocod:10,"3504398860243e":9,lazi:[23,19],million:[6,10],theori:[23,7,24],carl:24,org:[6,12,28,24,16,0,27,11],"___":[],mw_merten:[],care:[9,25,19,20,27],nthroot:[22,11],expm1:22,suffici:[7,10,20,4,18],"0x01508870":[],frequenc:7,honest:1,recov:[22,6,13,0],turn:[20,0],"79e":17,place:[19,12,20,14,23,7,4],principl:24,imposs:[25,7,8,18],frequent:25,first:[6,19,12,20,13,22,15,7,27,24,25,10,4,26,0,16,28,11,18],origin:[22,10,18],directli:[6,25,23,24,9,10,0,17,28,4],carri:[19,1],onc:[7,4,18],arrai:17,"106169926814270418999315e":0,fast:[6,20,22,28,7,24,25,16,26,27,4,18],symmetri:[9,24,16,20,11],oppos:0,modulo:[22,8,2],ring:28,open:28,angular:7,size:[6,19,25,10,26,18],given:[0,4,6,7,8,9,10,11,12,13,14,16,17,18,19,20,22,23,24,25,26,27],"0x016be9f0":[],cotang:[14,10,21],"27287187546220705604627e":0,workaround:4,"0x013af4f0":[],whitw:0,"0000005769149277148425774499857j":0,"0x013a24f0":[],adjac:12,nonintegr:[24,11,13],"290402449901174752972486e":9,whitm:0,necessarili:[10,8],averag:[],circl:[22,23,7,24,26,0],"8503366631752726568782447j":0,conveni:[6,19,22,23,24,25,0,17,4,18],includ:[28,6,19,20,21,22,14,15,24,9,25,16,2,0,27,23,11],hue:19,especi:[25,27,28,4],copi:[19,17],"0x0145e070":[],nonsmooth:[26,20],specifi:[19,7,8,24,10,26,27,17,4,18],mathworld:[6,23,7,24,9,4,0,11],hypergeometr:[5,13,15,24,9,16,2,0,23],"62e":17,borwein:[7,24],quad:[20,13,22,14,15,7,24,9,16,26,0,3,23,11,18],"0x01338030":[],than:[6,19,12,22,14,7,8,24,9,25,1,10,11,26,0,27,17,4],wide:16,"0x015045b0":[],f_l:[],nstr:[6,19,17],"939717517906339193598719j":16,"8598304758094664213e":27,posit:[19,22,23,7,8,24,9,25,1,10,26,27,16,17,11],"237132026969293954162816e":6,seri:[5,6,7,21,20,13,22,15,3,24,9,19,16,2,0,23,11,4,18],pre:[],analysi:[19,11],sai:[15,11],"75888275702l":10,pro:27,anywher:0,"0x0133d1f0":[],dash:19,convert_lossless:17,notimplementederror:24,"0x0145e0b0":[],slac:[],"8952500412050989295774e":16,engin:[10,4],techniqu:[],bailei:[7,10],"715826296033590204557054j":24,"0x0138bc30":[],note:[6,19,20,13,22,14,15,7,8,24,9,25,1,10,11,26,27,16,28,4,18],tanhsinh:7,"1e1000000":0,denomin:[10,11],take:[19,13,22,14,28,7,0],kerner:12,begin:[11,13],sure:[22,28],normal:[13,25,14,9,1,16,2],track:[19,25,1,27],nprod:[23,19,4,3],beta:[24,2,11,0],pair:[19,20,7,1,10,0,27],"45285242480185e":11,"0x01380f70":[],"1998650072605976600724502j":13,subinterv:[19,7],anewton:27,round_nearest:[],hankelh2:[],mnorm_oo:[],g11:24,"0x013478b0":[],axi:[6,22,8,24,9,16,0,11],salt:[],pparam:[],"0x015b8f70":[],wynn:4,show:[19,20,22,23,10,0],leibniz:4,logarithmicintegr:9,cheap:[7,17],bright:19,gegenbau:[2,13],threshold:25,corner:22,rotat:[16,21],onli:[6,19,22,14,7,8,24,9,25,10,11,26,0,27,17,4],explicitli:[25,6,19,10,4],ratio:[23,6,10,2],"5266839997214j":15,proportion:25,state:[9,19],"973341637511505389128708e":16,parametr:22,dict:10,"0x1c500c8":19,thompson:16,analyt:[6,20,7,24,16,26,0,27,11,18],sum_k:[],nearli:20,variou:[13,22,23,7,0,17,11],get:[6,19,28,7,24,9,1,10,27,18],pegasu:27,repr:[25,19],"71150868372136e":16,"0x01397bb0":[],cannot:[25,14,28,1,24],progress:[19,7,4],infiniteproduct:4,requir:[19,25,14,15,7,24,9,10,4,26,0,11,18],ramanujan:[6,11],"08848758376254e":9,yield:[22,27,26,4],sum:[5,6,19,22,23,7,24,9,25,11,0,3,17,4],"0x0138c030":[],scientist:4,"60784095465201e":11,through:24,where:[6,19,12,20,13,22,14,15,7,8,24,9,25,10,11,26,0,16,23,4],"67963e":20,wiki:[27,12,24,11,0],meijer_g:0,"822879187542699127327782j":0,"0x2b5f0c8":[],assumpt:7,"0x0133c570":[],"66238556639137e":[],"49052338550226e":6,nonstandard:20,concern:[17,10],infinit:[6,19,22,15,7,9,25,1,10,11,23,4],"078258353474186729184421e":9,nonreal:27,detect:[28,10,4],"0x013b67b0":[],"49795891462086e":11,"0x01a162b0":[],enumer:6,quadraturerul:7,"680424678918e":24,enough:[6,25,1,10,0,27,4],"9253203909477023089e":[],"31102877714605990523242j":15,between:[19,22,14,28,7,8,24,9,25,1,10,27,16,4,18],"import":[1,0,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],spars:17,comp:[22,16],amplif:7,ln2:24,come:25,ode_step_rk4:[],noconverg:0,pertain:24,mani:[6,11,20,22,23,7,9,25,19,10,2,0,27,4],"189190365227034385898282e":0,unrecogn:19,among:[12,10,11,16],acceler:[27,4],rescal:[7,16,0],inspir:10,period:[14,15,7,24,16,23],lacim:24,pochhamm:11,twin:[23,2],featur:[5,23,19,20],cancel:[20,22,7,8,9,0,27,4],poli:20,needlessli:[],fib:[6,23],most:[6,19,22,14,15,8,24,9,25,10,11,0,27,17,28,4],"0x01342b30":[],invert:[22,0],ucla:0,valueerror:[15,8,9,27,17,11],schroding:16,arcsin:14,thousand:7,andrew:24,"0x01379c30":[],catastroph:22,"8382249570693706959264156336481764738284680928013e":6,weierstrass:11,those:[22,14,19,10,24],"case":[19,27,13,22,23,7,8,24,9,25,10,11,0,16,17,28,4,18],"50j":[9,16],add_package_repositories_to_yast:28,casi:24,whittak:[2,11,0],"003238627353609801446359j":14,trick:7,"4949812409615803110051e":16,p155:24,qr_solv:17,"1256256609322773150118907j":0,"0x01394b70":[],region:4,advantag:[7,26,4],stdout:19,bcller:[],henc:[7,1],"04124253736317e":16,good:[19,20,15,7,9,1,26,27,4],ivp:18,kright:[],"12th":22,"04120098628857412646300981j":14,develop:[28,10],"887705114889527446891274e":0,author:[9,15],"0x01395bf0":[],admit:1,same:[19,20,13,22,14,15,8,24,9,25,1,26,4],binari:[19,25,28,1],html:[6,23,7,24,9,10,11,0,28,4],"417977827655098025684246j":0,document:[5,6,19,22,14,23,7,8,24,1,0,27,28,4],hermit:[2,13],"0447701735209082j":7,"27s_method":[],finish:[25,28,10],"4342944819025j":16,closest:[22,27],kelvin:[16,2],"2831853071795864769252868j":[],siegel:[2,24],"04914370344703j":9,companion:19,coffei:24,improv:[27,6,7,20,4],solvabl:7,"35185474521784529049653859679690026505229177886045j":24,appropri:[28,7,11,4,0],moder:6,without:[9,19,6,7,8],gain:[],"6313342832413452438845091j":15,model:25,dimension:[27,18],"437j":16,"0x0134e9f0":[],execut:19,excel:4,stegun:[9,13,16,0],"0x0150a8b0":[],gausslegendr:7,"0x0138c1f0":[],"2773099198055652246992479j":24,"0x0138ebb0":[],polish:27,runtim:28,speed:[20,25,28,27,17,4,18],"684053288183046528703611j":16,"434290j":16,clausenc:[],miscellan:10,"4f1":0,autom:10,except:[6,19,22,14,15,7,9,25,4,0,27,23,11],param:0,estimate_error:7,identif:[5,10],color:19,notori:4,"33333333333333e":11,momentum:[],real:[6,19,12,22,14,15,7,8,27,24,9,25,10,2,26,0,16,17,11],psi:[23,24,11],around:[20,22,7,24,16,26],hypothesi:6,read:4,"248376x":[],"3197663987712e":11,"0x015075b0":[],"0x0132c130":[],"21j":24,sum_:[],"5625e":24,exploit:7,integ:[5,6,19,13,22,15,11,8,24,9,25,10,2,0,16,28,4],"0x013988b0":[],mpmath:[1,2,0,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],either:[19,25,28,7,24,10,4,0,11],output:[19,25,6,7,10],tower:22,manag:[25,28],"0x015074b0":[],polylog:[9,24],"02203963877155499262848j":24,constitut:0,nonzero:[12,13,22,24,25,1,26],ellip:[15,0],"109227893755336597979197j":14,definit:[6,13,22,14,15,24,9,4,0,23,11],achiev:4,exit:[19,10],"0x0145a6b0":[],cylindr:16,bessel:[5,7,16,2,0],"0x0134d9f0":[],refer:[6,12,25,15,7,24,9,16,4,26,0,23,11,18],besselk:[16,0],besselj:[16,0],power:[5,22,24,25,10,2,17],"49952562843408e":19,garbag:4,ration:[6,20,13,22,24,9,25,10,4,0,11],orszag:4,fulli:18,comparison:[6,7,0],mdnewton:27,central:[23,26],opensuse_11:28,opensuse_10:[],aco:14,meaning:[],"606j":0,chop:[6,19,20,13,22,14,15,21,24,9,16,0,11],degre:[20,13,14,23,7,10,2,0,18],"166227124177353j":22,act:25,luck:10,hyp2f3:0,hyp2f2:0,hyp2f1:[15,0],hyp2f0:0,effici:[22,15,7,8,24,25,26,0,27,23,4],elementari:[9,16,24,11,0],"75x":[],terminolog:25,invers:[21,22,14,7,9,1,10,2,27,17],"75e":[6,17],strip:24,"75j":16,psi2:[],your:[5,28],log:[27,22,14,23,7,8,24,9,25,1,10,11,0,16,4],area:[23,7],omega:[9,7],overwrit:[],start:[22,27,7,16,21],"005753848733883879742993122j":0,interfac:[25,28,4],low:[6,20,1,10,0,27,18],strictli:[7,1,24,0],svn:[],monoton:[14,4],verbatim:[10,4],linalg:17,mantissa:[25,19],tupl:[6,19,12,25,7,24,0],diffun:24,oscil:[7,20,4,18],"0x01398c70":[],longer:[18,10,13],ludicr:9,tripl:7,bullet:10,possibl:[20,22,15,8,25,1,10,26,0,27,17,23,11,18],"default":[19,25,28,7,8,24,10,26,27,4,18],mpmathifi:[19,27,13,0],"71678149306807j":24,"34814309345871e":22,connect:[16,24],taylor:[6,12,20,13,22,14,3,24,9,16,4,21,0,11,18],creat:[19,5,1,17],certain:[1,10,24,0],pole:[13,14,24,9,0,11],"7158262960335902045570541j":24,cbm:[9,0],littlewood:23,"925320392280406229e":6,decreas:[14,7,16,0,4,18],"0x013812f0":[],file:[5,28,19,17,24],girgensohn:7,legendreq:13,legendrep:13,"0x0196c070":[],denot:[6,19,22,23,7,24,9,0],googl:[5,28],mathematica:[14,7,11,13],field:25,binomi:[6,2,11,13],valid:[19,20,22,15,8,10,11],immens:11,cmath:[14,2],you:[5,19,28,7,8,24,1,10,27,17,4,18],massless:[],d2f:27,isint:19,sequenc:[13,25,24,1,4,26,11],symbol:[10,11,4],"1e1000":[9,8],"0000000001e":8,multidimension:[27,17],polynomi:[5,6,7,12,20,13,3,24,9,10,2,0,11,4,18],isinf:19,peak:7,"0005200017201681152909000961j":16,reduc:[6,13,22,24,9,25,10,4,0,16,11],directori:28,"07595200133501806872408048j":11,descript:[19,7,8],tricki:25,laplac:16,potenti:[22,16,0],acsc:14,togeth:18,represent:[5,6,19,25,15,8,24,9,16,11,0,23,4],all:[6,19,12,20,13,22,14,28,7,27,24,9,25,1,10,11,26,0,16,4,18],messi:0,lack:[25,17],scalar:[17,18],correl:25,mp2:19,abil:[25,19],acosh:21,"728805278735270407053139e":9,follow:[28,19,12,22,15,7,8,27,24,9,25,1,10,11,26,0,16,23,4],disk:[15,4],"9294486669502295512503127j":16,grampoint:24,sympi:[17,5,28,10],hypxfx:0,"16470269330255923143453723949e":22,program:6,present:[6,19,7,8,10,4,11],"0x01375c70":[],discontinu:7,"41421j":11,"60849e":[],introduc:[25,6,18],mpf:[6,19,20,22,23,8,24,9,25,1,10,11,26,0,16,17,28,4,18],liter:[19,1,24],mpc:[23,19,8],bitcount:25,fals:[19,12,20,22,7,8,24,9,1,10,11,27,4,18],faq:25,mpi:[6,19,22,14,1,17],util:[5,19],"71130938718796e":9,failur:28,fab:8,fac:[6,13,22,23,24,9,16,4,0,11],"_1f_1":[],"0x0132f070":[],list:[6,19,12,20,22,15,7,24,10,26,0,27,17,28,4],one_tenth:[],emul:[25,19],cosin:[20,21,14,7,24,9,16,0,18],small:[6,19,22,25,10,26,0],ellipt:[5,15,2,0],node3:10,"0x01390530":[],dimens:[7,17],unnorm:14,fresnelc:[9,19],rate:[27,7,11,4],design:[7,1],pass:[19,20,22,28,7,8,24,0,27,4],further:[19,25,28,10,26,0],whenc:[],"158j":16,what:[1,10],nonlinear:[27,18],richard:24,diag:17,section:[6,19,24,9,16,0],advanc:[25,17,26,4],"_jacobi_theta2a":[],delet:[28,7],sinpi:[14,23],version:[19,20,13,25,14,28,11],intersect:27,rerr:6,consecut:[7,24,11,4],"22568799288165021578758j":9,method:[6,19,12,22,7,25,10,26,27,17,4,18],contrast:4,maxstep:[12,10,27],"031911949062334538202567e":24,legenq:13,legenp:13,"19j":16,strong:[7,4],modifi:[14,16,2,26,27],valu:[3,1,0,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],search:10,"0x01397f70":[],indetermin:19,twinprim:[23,2],polyexp:[6,24],amount:[25,6,7,11],doctest:[19,20,22,28,7,24,9,1,10,27,17],action:19,"002472407104546216117161499j":0,narrow:1,"293142504363642687204865e":11,magnitud:[6,19,22,7,8,24,25,10,16,17,4],quotient:[8,11,4],via:[25,14,28,24,9,0,11],primit:[22,6,1],"while":[6,19,25,0,27,11,18],int_0:[],put:18,bernfrac:6,famili:[9,27,19],establish:[5,1],crandal:24,select:[13,22,7,4,26,11],"326146j":[],distinct:22,regist:25,two:[6,12,20,22,14,15,7,8,27,24,9,25,1,10,2,26,0,16,28,4,18],taken:[25,7,24,16,4,26,0,11,18],stieltjesgamma:24,minor:25,more:[1,0,4,6,7,9,10,11,13,14,17,18,19,20,21,22,23,24,25,26,27,28],flat:17,diamond:7,desir:[7,4],hundr:7,c_l:[],"02074960467222823237055351j":16,flag:[28,8],int_l:[],"0x0138c870":[],particular:[12,25,23,24,10,4,11],known:[6,22,23,24,9,25,4,26,0,27,11,18],cach:[6,7,16,18],elliptice2:0,"0x0196d9f0":[],none:[19,22,7,25,10,27,17,4,18],jdn:15,eta:[16,24],deq:13,det:6,erfinv:9,"0x016bf7b0":[],remain:[12,11],nonsingular:16,multiprecis:[],q_lim:15,"890569218254486878220752e":0,def:[22,27,19,20,0],"0x0134ae70":[],coulombc:16,dobinski:6,coulombg:16,coulombf:16,accept:[19,17,18],minimum:[27,21],"46458120882585e":11,pointwis:20,sharp:[19,7],"431j":[],"2908503133698e":[],string:[19,25,1,10,27,17],huge:[22,15,24,25,16,0],cours:[7,9,1,4,17,11,18],prod_:[],rather:[26,7,24,11],anoth:[7,1,16,26,27],comfort:17,csc:[14,2,24],divis:[25,8,1,10,0,4],reject:4,jborwein:7,scienc:28,simpl:[6,19,12,20,22,14,7,24,9,25,10,4,26,27,16,11],resourc:25,primezeta:24,algebra:[5,19,1,10,17,11],variant:[27,2],internet:24,"0x013819b0":[],reflect:24,plane:[19,14,15,8,24,0],"691337610097577791134j":13,varianc:9,associ:[24,13],gaussian:[9,7,11],circumst:22,"short":[25,19],ani:[28,6,19,12,20,22,15,7,27,24,25,1,10,11,26,0,16,17,23,4,18],sech:21,preferr:10,caus:[7,17],atan2:[14,8],zerodivisionerror:[22,27,0],"0x013b35b0":[],help:[28,0],soon:[25,26,4],pseudorandom:4,paper:[10,24],firrst:11,gammaprod:[11,0],variat:26,suffer:22,"0x01391c30":[],paramet:[13,15,24,9,16,26,0,11],style:19,altzeta:24,borwein_zeta:[],brows:28,rapidli:[6,7,24,9,4,0,11],jacobi:[6,15,2,4,13],cross:15,might:[22,23,7,8,25,27,17,28,4],scipi:[27,11],"return":[6,19,12,20,22,14,7,8,24,25,10,11,26,0,27,17,4,18],"49j":0,"59947894041409j":12,siegelz:24,complain:25,"4f3":0,ldexp:[19,8],gamow:16,level:[7,1],"0x012ed130":[],instruct:[28,20],easili:[10,13],absmin:19,radian:[14,23,2],radial:16,found:[12,25,14,15,10,27],truncat:[12,20,25,7,10,0],kutta:18,"0x01310630":[],weight:[13,7,20,4,0],needless:15,hard:[],"0x017535b0":[],procedur:4,expect:[27,17],quantum:16,beyond:[20,4],todo:[22,4,18],standard:[20,25,14,15,7,9,1,10,2,26,0,3,17,28,11,18],"0x013429b0":[],meijer:[2,0],robert:4,"0x014615b0":[],research:11,print:[5,6,19,12,22,14,28,7,8,27,24,25,1,10,11,26,0,16,17,4,18],"0x0137ff70":[],zeta_t:24,"596619701076529803290973e":16,"0x0139c570":[],"1084662449961914580276007j":13,"755146243738946045873491e":9,guess:[27,10],pub:[],reason:[25,23,7,18],base:[6,22,23,7,24,10,2,0,27],ask:25,approach:[9,6,16,24,4],"303985255686378497193063e":0,"86724550696231e":16,"866025j":22,mpi_to_str:19,exponenti:[5,6,11,22,14,15,7,24,9,25,10,2,26,0,16,23,4],"0x012ec130":[],perhap:25,"202966666673054671364215j":24,"06154836525312066938147793j":0,assign:[],integrand:[9,7],singleton:7,"0x013b2630":[],"22044604925031e":[17,12],perturb:[6,0],famou:[10,24],mersenn:[22,19],number:[1,2,0,4,5,6,7,8,9,10,11,12,13,15,16,17,19,20,21,22,23,24,25,26,28],placehold:11,smaller:[25,17,19,12,27],done:[6,25,7,24,17,11],nsimplifi:10,"58810701527j":11,"6141851464j":0,idea:[15,10,26,4],differ:[6,19,13,25,23,7,8,24,1,11,26,0,27,4],quadt:7,nome:15,interact:[25,5,28,19],construct:[19,24],contra:27,transcendent:[25,23,10],"5863603889018621585533j":16,"33262283196162e":11,scheme:[25,7],"86e":17,store:[19,17],"792526803190927323077905j":0,stirl:[11,4],statement:19,relationship:6,mnewton:27,"33333e":[22,14,6,20,21],part:[5,6,19,12,22,14,7,8,24,16,2,0,11],"32579597597705e":11,"950930337531768015892987e":0,sign:[19,25,14,7,8,24,9,1,26,27,4],plusminu:19,kind:[13,22,15,7,16,0],"2f0":0,contrari:25,doubli:[15,7,4],cyclic:22,"18j":19,remov:[25,19,10,4],"_jacobi_theta3a":[],reus:7,str:[6,19,22,23,25,17],toward:[25,27],openopt:27,randomli:19,comput:[1,0,4,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27],"008156449464604044948738263j":11,packag:[28,19],aperi:[23,2,11],option:[5,19,20,22,28,7,8,24,25,26,17,4,18],"0x01399030":[],built:[25,27,19],lib:[25,28],"013370403397787023602j":24,self:[],speedup:7,also:[1,2,0,4,6,7,9,10,11,12,13,15,16,17,18,19,20,22,23,24,25,27,28],libhyp:[],build:28,jacobian:27,npdf:9,"0x01386c30":[],"0x01549e30":[],distribut:[9,7,2,11],"875060251748226537857298e":9,setuptool:28,jsn:15,"0702051v1":16,reach:[10,20],t_list:[],alpha:0,"62422642529928e":[],clear:[7,0],cover:19,roughli:[6,19,22,23,7,9,25,16,26,10,4,18],"0x013ae530":[],"0x0145f070":[],exp:[19,27,20,13,22,15,7,24,9,25,1,10,11,26,0,16,23,4,18],usual:[19,25,28,7,24,10,0,27,17,4],"410032405664160838288752j":11,"54052086914493j":11,"4000000j":16,chebyshev:[13,2,20,3],"11604466157397267043655j":24,hyper:[9,24,0],phenomenon:[],carefulli:[],fine:16,find:[5,12,22,24,10,4,3,27,11],"4985390447553234305e":24,trap_complex:19,pretti:[0,4,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,26,27,28],solut:[27,20,13,22,23,7,24,1,10,0,16,17,4,18],bernpoli:6,"0x01310330":[],factor:[19,25,15,24,9,16,0,27,17,23,4],"0x0134b970":[],"0x20fd0c8":[],express:[6,22,14,24,10,11],"2f1":0,"66e":17,coth:21,arxiv:[16,24],"30566371247811e":16,hankel2:16,dtc:24,hankel1:16,common:[19,25,23,7,2,0],crd:7,nowher:[],set:[5,6,19,12,20,13,22,28,7,8,25,1,10,11,26,0,17,4,18],seq:4,"905169561300910030267132e":0,mutabl:17,fneg:8,see:[1,0,4,5,6,7,8,9,11,12,13,14,15,16,17,19,20,22,28,24,27,23],sec:[14,2],arg:[9,19,8],close:[6,19,20,13,22,15,27,24,9,25,10,4,0,16,11],contour:0,analog:[9,23,19,24,11],barn:[23,11],"499471750566824369520223e":24,"094434067582614099516304e":[],evalaut:[],"0x01357430":[],"61398543581249e":11,someth:[15,26],smallest:[8,20],"0x0135f7f0":[],nontrivi:[27,24],"131705322874965310390701e":0,"0x013749f0":[],altern:[19,13,22,15,7,24,2,26,0,27,28,4],signatur:19,"232856260909107391513108e":11,unitroot:[22,6],numer:[0,1,3,4,5,6,7,9,10,11,12,13,16,18,19,20,22,23,24,25,26,27],"0108575801457j":24,isol:[],"75527e":4,matplotlib:19,complementari:[9,6,24],solv:[13,22,24,25,16,3,27,17,18],froberg:24,"31e":6,both:[19,20,22,23,7,8,24,9,25,1,10,2,0,28,4,18],last:[19,22,15,8,24,9,4,0,27,17,11],nonrigor:6,"46875e":11,"05658474496e":11,context:[15,19,8,11],"0x01380270":[],"915965594177219j":24,whole:22,load:28,simpli:[19,22,25,10,0,4],"0x0196e9f0":[],point:[1,2,0,4,5,6,7,8,10,11,12,13,14,16,17,18,19,20,22,23,24,25,26,27],residu:[7,17,24],suppli:[19,7,10,24],"_jacobi_theta2":[],"_jacobi_theta3":[],zeta:[5,6,19,23,24,2,27,4],coincid:24,rac:[],"48071721019185e":16,nogmpi:28,sine:[20,21,14,7,24,9,16,0,18],due:[6,25,7,24,17,4],calculu:[5,12,20,26,3,4],sinc:[6,19,13,22,14,15,7,8,24,9,25,10,2,0,11],"07269254613282301012735797j":0,strategi:25,ei_a:[],thresshold:[],b_n:[],fire:28,"0x016bc9f0":[],imag:[19,8,11,0],convert:[19,22,14,15,8,25,10,17,23,4],"0x01397bf0":[],coordin:16,func:[],demand:25,b_q:[],norm_p:[],look:[25,28,10],"168906959966564350754813j":14,erron:[14,28,19,10],kwarg:[6,19,21,22,14,15,7,8,9,10,11,0,27,4],pace:11,"0x01378ab0":[],abov:[9,28,10,24,13],error:[19,5,6,11,12,20,21,22,7,8,9,25,1,2,0,27,17,4],"0x016c07b0":[],"0x013935b0":[],loop:[],propag:1,larger:[6,25,24,9,1,10,26,11],"3619719871407039993e":[],vol:16,von:6,"89e":17,quadrat:[12,7,10],tripli:26,vanish:7,"93147180559945e":22,decor:19,minim:[17,10,27],"46072418957528e":9,ldot:[],"9219851739689e":[],"0x015bbf70":[],higher:[25,8,24,1,4,0,11,18],optim:[5,6,20,3,0,27,4,18],wherea:9,"0220396387716j":24,user:[25,28,7,10],expint:[9,0],"7018j":11,riemannr:6,typic:[19,12,25,7,4,26,0,11],"1000j":[22,16,24,13],recent:[22,15,8,24,9,0,27,17,28,11],subpackag:28,lower:[9,25,10,4],task:[19,7],equival:[6,19,21,22,14,15,8,24,9,25,4,0,11],"0x013859f0":[],older:25,chebyu:13,entri:4,parenthes:6,person:24,expens:[6,20,22,7,26,18],academ:20,"107491j":9,a_1:[],cuboid:7,pylab:19,"0770637306312989892451977j":9,glausen:[],shape:7,spuriou:10,"67j":16,"67e":17,failsaf:[],cut:[6,22,14,28,9,0,11],complexnumb:28,theoret:[5,6,2,20],"83493347225108e":11,rgb:19,quadratur:[5,20,13,7,9,3,4],theorem:[9,22,6],input:[5,19,14,28,7,10,0,4,18],euler:[4,22,23,7,24,9,10,2,11],ight:[],obsolet:28,format:[17,7,12,20],big:7,"0x01381770":[],catalan:[23,24,10,2,11],bit:[19,25,7,8,24,10],"399196580646054789459839j":9,a_j:[],"160893281017115450519948e":16,"76e":6,"0x01330070":[],success:[16,7,10,4],"0x013a0530":[],"0x013853b0":[],"9328495143101e":11,signal:7,"4000j":[],resolv:7,elaps:19,collect:19,princip:[9,14,22],popular:25,"__new__":7,interestingli:7,encount:[15,19,11],doubleintegr:7,from_float:[],some:[6,19,27,22,14,15,7,24,9,25,1,10,11,0,16,17,28,4,18],back:[22,25,28],"186339621747697j":16,understood:[16,13],unspecifi:22,sampl:[19,24,20,4],brent:27,scale:[22,27,26],stieltj:[23,2,24],"850502209186044j":11,"0x0138b9f0":[],"510544741058517621110615j":0,per:[27,7,18],"06100816202125885450319632j":9,mathemat:[5,6,11,22,14,23,7,25,19,10,2,17,4],larg:[6,11,13,22,7,8,24,9,25,19,10,2,0,16,17,4,18],reproduc:16,appellf1:0,oversampl:[],machin:[25,17,10,20],previou:[7,4],run:[25,5,28,7,10],"0x0138b5f0":[],word:[22,19,10],"675159751729877682920301e":13,step:[19,22,28,7,26,27,4,18],dirichlet_eta_funct:24,"983617742029605093121118j":9,nonrat:24,"_method":27,subtract:[25,8,20],meijerg1:0,stieltjesconst:24,constraint:10,morri:4,"46923988977204e":6,memori:[25,8],"365499358305579597618785e":0,"0x018a8730":[],asech:21,cecm:[10,24],gamma:[5,19,22,15,24,9,16,2,26,0,27,23,11],"012757178975667428359374e":13,"__future__":19,primarili:7,"365981529122220091353633e":0,p_n:[],within:[25,28,7,24,10,26,27,4,18],ellipsi:[19,22,7,1,10,27,17],ensur:[25,27,6,19],triangl:11,riemannzetafunct:24,"0x019715b0":[],question:0,"long":[25,10,4],custom:[19,25,7,8,24,10],"935753855797342532571597e":0,borel:[],arithmet:[5,6,19,12,22,14,23,8,25,1,10,2,17,28,4],prettier:19,forward:[10,4,0],"0x0134c8f0":[],int_:[],libmpf:25,properli:[7,11],repeatedli:19,gauss:[13,7,0],decomposit:[17,8,2],reed:24,translat:[25,10],expintegralei:9,atom:10,line:[19,14,7,24,27,17],mitig:10,"78309e":4,infj:15,consist:[],confusingli:0,access:17,fdiv:8,"0906111371962375965296612j":14,complex_numb:28,with_stat:19,similar:[27,21],"0x013ab5b0":[],findpoli:[5,10],constant:[5,4,13,23,7,24,10,2,16,11],thereabout:19,"625115880451325002151688j":9,repres:[19,22,14,23,8,25,1,10,27,17],incomplet:[9,2,11,0],poussin:23,behavior:[25,24],journal:4,nonsymmetr:20,"0x016a89b0":[],"00000008274037e":22,polygon:22,"0x01317230":[],sequenti:6,nan:[19,25,14,23,0,11],"1e100":0,djtheta:15,jcn:15,nice:[27,7],mertensconst:23,"765587078525922j":24,eval:[25,19,10],asec:14,formal:[24,0],preconvert:[],"0x0198d2f0":[],agm:22,"972260393822275434196053j":13,zeros1:24,algorithm:[6,12,22,7,24,9,25,10,26,0,27,4,18],inaccuraci:17,evenli:19,tradeoff:18,delta:[6,1],nasa:24,"0x0196e1f0":[],maxcoeff:10,transform_nod:7,far:[25,6,24,4,0],"100000j":9,extrapol:[5,7,4,3],jtheta:[6,15,4],"0x0132e070":[],scratch:25,ellipk:[15,23],schoenfeld:6,bellexp:[],"91713e":16,edu:[24,0],takrn:[],"71e":17,entrywis:17,cython:28,"1415926535897932385j":24,elsewher:[24,11],send:28,nonposit:[24,11,0],"0x014de570":[],"1e1000000j":0,fly:[],"01e":17,sympifi:10,"34294481903252e":9,wave:[7,16,2],"0f1":[],volum:4,"999977909503001j":9,implicitli:[20,11],glacial:11,"58129703509927e":[],"0x18770c8":[],complic:4,fewer:[7,18],"try":[19,25,7,10,27],"09136296657021e":6,dealt:7,"0x0138bf70":[],"23936276195592e":14,pleas:[27,28],impli:[14,16,26,24],nonconverg:24,natur:[22,23,17,2,0],"44j":[],investig:[10,24,4],"21699e":[],odd:[6,20,21,22,24,9,25,16,4,11],append:[19,4],"656628229175902018939005e":16,compat:[25,5,28,17],index:[6,22,28,4,17,11],"0x0139d1f0":[],compar:[9,25,17,4],slight:7,polyfit:[],experiment:[27,7],secant:[14,27,21],"021799872770764149793693e":0,superstit:25,despit:[25,10],len:[22,6,19,4],bodi:[],lambertw:[22,27],"59e":17,gmpy:[5,28],sinh:[7,4,21],ubuntu:28,vertic:[22,19],implicit:0,"066421087689197632388731e":16,remark:20,convers:[25,14,23,19,2],"3283224323946162083579656j":0,ctx:[16,7,8,4,0],"1f1":0,later:[28,19],converg:[6,12,20,22,15,7,24,9,0,27,23,4,18],"0x0145e0f0":[],chang:[19,25,28,7,8,24,26,27,17,4],chanc:25,hardi:23,"58775110440458732748279j":9,"117867654j":26,appli:[19,21,25,23,24,1,10,4],approxim:[5,6,19,12,20,13,22,23,25,10,4,26,3,27,17,28,11],inequ:[5,6,1],apt:28,"0x0133b030":[],"58778525229247312917j":12,"3448325764012e":6,michel:16,"0x0138e2b0":[],nest:[7,17,26,11],from:[1,2,0,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],"163368465314934589818543e":0,zip:[28,19,26],chi:[9,24],doubl:[22,25,6,7,11],upgrad:28,next:[12,10,4],websit:[28,24],few:[6,19,13,22,7,24,10,4,11],"83675545731519e":16,nprint:[6,19,12,20,13,22,14,15,21,8,24,9,10,11,26,0,16,17,4,18],"28318530717959j":7,remaind:4,sort:12,kinkelin:[23,11],deflat:[],pfq:[],trail:25,"33j":0,"33e":[6,17],"66577118985331e":19,uwo:22,account:8,retriev:[15,7,0],alia:[22,6],arang:[19,4],cambridg:11,"0x016bb9f0":[],salam:4,obvious:25,calcbn:6,squarefre:24,"19850014994_1985014994":24,"849835186175096516193e":0,tau:15,quickstart:5,tar:28,"05494e":19,process:10,fourierv:[20,3],sudo:28,"0x019f6570":[],high:[28,6,19,12,20,22,15,7,24,25,10,26,27,23,4,18],onlin:[22,28,7],tan:[14,1,21],analyz:[],everywher:14,gcc:25,"883714220959876246415651e":0,polyexponenti:[2,24],uqam:24,prevent:10,occur:[9,25,10,4,0],cbrt:[22,19],subdirectori:28,findmin:27,instead:[6,19,20,13,25,23,7,24,1,10,17,28,4,18],"94e":6,sin:[19,20,21,22,14,15,7,24,9,1,16,4,0,27,23,11,18],"0x334c0c8":[],sommerfeld:[],singular:[19,20,22,14,7,9,16,26,0,17,4],"1347251417347j":24,"0x013939f0":[],notebook:28,"905250692824046162462058e":0,redund:25,physic:16,alloc:25,"083660630910611272288592e":9,essenti:[6,20,13,14,15,21,8,9,10,4],"875060250875106915277943e":9,correspond:[20,13,25,24,16,26,4],element:[6,19,12,0,17,4,18],issu:[28,20,22,23,25,10,15,4],allow:[19,13,25,28,7,8,10,0,17,4,18],"052951783922142735255881j":0,least:[5,6,20,7,8,10,17,4],sigmoid:21,report:28,own:[22,14],perfect:[7,4],"096964974460199200551738j":0,chosen:[19,22,24,26,0,11],zeroth:24,gammabetaerf:[9,11],csch:[4,21],trvial:[],infrastructur:7,decai:[7,16,4],differint:[16,26,3],therefor:[13,25,7,4,11,18],fourth:24,"13e":17,nonneg:[6,13,25,8,24,11],dal:7,bernoulli:[6,2],ferguson:10,"159388148811981535941434e":0,assess:[],"27_method":[],anyth:19,edit:11,hypergeometricfunct:0,"169178177065714963568963e":0,sincpi:[14,23],"98305038640398e":[],astronom:11,"1684e":27,mode:[25,28,19,8],modf:8,fprod:[6,19,4,3],"0x01339b30":[],"61349954245e":20,map:[17,0],bump:7,barnett:16,"0x01341eb0":[],combinatori:[5,6,2],frac:[],special:[6,19,13,22,15,24,9,25,16,2,0,17,23,11],out:[19,20,28,7,1,0],variabl:[28,15,7,2,0],"0x014d74b0":[],matrix:[5,19,1,27,17,4],"0x013a67f0":[],automag:23,categori:[25,0],"0x0138b8b0":[],"23828e":0,suitabl:25,rel:[9,6,19],hardwar:25,kerner_method:12,clsin:24,matric:[19,5,1,17],offprint:22,insid:0,"74266443803466j":11,standalon:0,control:[25,19,8,18],almosteq:19,"9038644233367868273362446j":24,dictionari:17,releas:28,afterward:[27,19],"38889e":14,ultraspher:13,dirichlet:24,transposit:17,"15779412229419e":11,unwant:10,could:[25,27,10,20,13],david:10,counterpart:4,length:[7,24,20,18,0],enforc:8,psi0:[],psi1:[],"0x013572b0":[],softwar:[14,28,11],"72510874248161608216j":24,christoph:[],"34584913683906e":0,"1240770953126831093464055j":16,fmul:[16,8],date:28,"1e7":9,"24575026015369e":19,facil:[23,10],"1347251417346937904572519836j":27,liouvil:[16,26],"10x":[],strict:[28,10],unknown:10,licens:28,system:[25,27,28,17,18],wrapper:[27,10],"14159265358979j":22,termin:[13,4,0],man:25,"final":[19,25,28,27,17,4],"0x018edbb0":[],"0x0137e9b0":[],"426j":24,exactli:[6,19,22,14,23,8,9,25,1,0,4],"43433j":16,stupend:6,bei:16,"65j":16,structur:13,charact:24,num:0,sens:[7,16,26],becom:[22,7,24,25,4,11,18],"45537085334512e":[],ber:16,"757089288053346261497686e":16,exhibit:24,falsi:27,have:[19,12,20,13,22,14,15,7,8,27,24,9,25,1,10,11,26,21,16,28,4],tabl:[25,16,10,24,4],need:[19,20,25,28,7,10,26,27,17,4,18],clco:24,border:4,ylim:19,"42236140124728e":11,"9253203909477020467e":6,bdiff:4,cparam:[],newtonian:27,min:[],diverg:[9,11,4,0],mid:[7,1],accuraci:[5,19,20,25,7,10,4,18],mix:19,builtin:[19,4],which:[0,4,6,7,8,9,10,11,12,13,15,16,17,18,19,20,22,23,24,25,26,27,28],fac2:[16,11],subject:10,singl:[19,22,14,15,7,4,26,0,17,11],unless:[6,0],who:25,"0x017cdd30":[],rigor:[6,17],realnumb:28,segment:[14,20],why:[25,19],hyp0f1:0,laurent:24,"32e":17,url:[28,24],inde:[15,10],"275758229007902299823821e":0,"400j":24,"35e":6,polygamma:[24,2,11],univari:[],determin:[19,6,18,0],fdot:19,"0x019709f0":[],hyperk:[],fact:[25,7,1,10,24],"0x01356370":[],"2464022641351420167819697j":16,text:[28,20,18],"12j":11,verbos:[19,7,10,27,4,18],"0x01394570":[],"0x013967b0":[],"2660553j":16,"5309210862485198052670401j":21,trivial:[27,23,13],"101124983878j":11,"20000000j":0,"989901335682408421480422e":6,locat:[27,28,12,24,13],nois:6,losslessli:[25,19],should:[5,19,12,20,13,22,28,7,8,24,9,25,1,10,11,26,0,16,4,18],manufactur:[],durand:12,won:19,suppos:7,"257913707524362408877881e":9,local:[27,19,24,18],pborwein:24,cube:22,"00000012791934e":22,notat:[15,0],familiar:8,heta:[],sh_:[],overdetermin:[27,17],extradp:[19,24],workprec:19,"141592653589793238462643j":9,nonrectangular:7,endless:10,"3475255449236e":16,enabl:28,organ:10,bisect:[27,24],mptype:8,"577879007912758274533309j":15,"33636415517321e":[],integr:[5,6,7,20,13,22,14,15,3,24,9,16,2,26,0,23,11,4,18],partit:[6,19],contain:[5,19,20,7,1,10,0,17,4],"8243465421j":[],shi:9,dpi:19,view:[15,12,0],"0x0132cc30":[],"03347835361657e":16,mpf_add:[],"0x0137f730":[],knowledg:[],"0x014372f0":[],temporarili:[19,7],"0x01343c30":[],particl:16,isnan:19,conjectur:23,correctli:[25,1,10,20],"32207626732144e":16,powm1:22,tend:[7,11],written:[6,18],"333333j":0,theta:[6,24,15,2,4],neither:7,predefin:23,kei:16,"13472514173469379045725j":24,moebiu:6,entir:[25,14,7,24,11],"32579620567308e":11,"2pi":[],argument:[1,2,0,4,6,7,8,9,10,11,13,14,15,16,18,19,20,21,22,23,24,26,27],"8068182256629216e":[],ker:16,addit:[28,20,22,15,7,8,24,9,25,16,27,17,23,4],hypercomb:0,staudt:6,"211322x":[],equal:[6,19,13,22,23,8,24,25,26,28,11],etc:[4,6,19,20,25,8,10,2,26,11],"07944x":[],instanc:[6,19,23,7,8,24,0],grain:[],equat:[5,27,20,13,22,15,3,24,10,0,16,17,11,18],"0343v1":24,psi4:[],comment:25,a_p:[],x_k:[],distinguish:25,whitmw:0,"700j":16,"0x0138b770":[],"46j":11,respect:[19,20,13,15,7,24,0,23],page_504:0,quit:[7,17],cauchi:9,slowli:[20,23,7,16,27,15,4],divid:[10,7,8,20],jit:[],compon:[8,2,26],treat:1,modif:6,"077063730631298989245j":[],immedi:4,partial:[19,22,7,4],apmath:22,presenc:19,"308937j":16,ridder:27,"2eta":[],deliber:[],extraprec:[19,12,24],x_0:[],"806818225662921587261496e":22,replic:7,hallei:[22,27],"05804937947429712998395177j":24,"3109263360275413251313634j":24,rectangular:19,defin:[1,0,4,6,7,8,9,10,11,13,14,15,16,18,19,20,22,28,24,25,26,23],overrid:19,"0x013a68b0":[],howev:[6,19,25,14,7,9,10,26,27,16,4],erik:24,helper:18,almost:[17,6,10],demo:28,"5th":12,"93665300979176e":11,archiv:24,adiff:4,substanti:4,greater:8,uniti:[22,14,6,12],let:17,welcom:5,"0x01379f30":[],sqrt:[6,19,12,20,13,22,15,7,24,9,25,1,10,11,26,0,16,23,4],python:[5,19,22,14,28,8,25,1,10,2,17,4],whenev:23,largest:[17,8,4],"0x018e36b0":[],antideriv:[9,22,16],difficult:[20,18],phi:[23,6,10,2,24],http:[5,6,12,22,23,7,27,24,9,10,11,0,16,28,4],cubic:27,expans:[6,20,13,22,24,9,16,0,27,11,18],effect:[25,28,19,20,4],khinchin:[23,2],phy:16,pdf:[22,7,24],"783578125755972803440364e":0,expand:0,"866025403784438j":22,"5599559310962e":16,off:[19,7,1,4],center:[22,7,26],"0x0138e0b0":[],"866025403784439j":22,well:[6,19,20,22,23,7,10,4,26,0,27,17,11,18],polyv:[12,10,20,3],exampl:[1,0,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,22,23,24,25,26,27,28],"11058e":4,choos:[9,27,7,17],undefin:[24,0],"47222e":14,latest:28,unari:23,"7298060598018049369381857j":13,distanc:16,"5118225699873846088344638j":21,"24570818422368e":11,less:[6,22,23,8,9,25,10,0,18],"135483865314736098540939e":22,"26j":16,"765587078525921j":24,obtain:[6,19,20,22,9,25,4,18],"2050415770437884900574923j":0,trust:17,simultan:[12,24,18],adv:22,rapid:20,preinstal:28,"114650753239580827144204e":16,bell:[6,2,24],"68162300487989766727122e":24,script:28,trigamma:[23,11],cleanup:12,"02107292320897e":16,densiti:9,oparam:[],match:10,"82246272698136e":16,max_degre:7,"49895233563961e":9,"0x01391530":[],know:[17,4],press:[20,11],similair:[],recurs:[19,6,7,13],recurr:[9,6,7,11,13],"0x0196f9f0":[],arbitrarili:[6,20,22,24,9,0,11],like:[5,19,12,22,14,7,24,9,1,10,11,26,27,16,17,4,18],lost:4,betainc:11,"22464679914735e":[22,23],weisstein:4,primepi:6,necessari:[25,7,10,0,27,11],"8565440833654995949e":24,lose:25,ncdf:9,page:[28,5,6,1,7],"198140234735592207439922j":0,nja:11,glaisher:[23,2,11],"539991603850462856j":0,logarithm:[5,6,13,22,23,11,24,9,16,2,0,4],growth:[23,11],"0x0174b530":[],"0x0138ebf0":[],proper:[22,14,7],guarante:[25,6,1],peter:7,b_1:[],librari:[25,5,28,17],win32:28,summat:[22,23,7,24,3,4],"0x01396bb0":[],lead:[22,12],struvel:16,avoid:[9,22,8,25,26],thank:10,estim:[6,12,20,22,7,9,27,4],leav:27,summand:11,"385040221241629041351886e":16,behav:[9,16,26,20,18],struve:[16,2],"11e":6,"92726697721369j":24,truth:6,"0x01333ef0":[],calc_nod:7,imaginari:[6,19,12,21,22,23,8,24,9,16,26,0],els:[27,15,19],docstr:0,"0x01393570":[],"0x013d5ef0":[],"0x01392570":[],although:[12,20,25,23,7,24,9,0,27,28,4],offset:9,"7th":22,simpler:27,hyperfactori:[2,11],about:[5,6,23,7,24,10,28,4],actual:[19,25,7,8,10,26,4],column:[17,4],odefun:[22,18,3],sumem:[4,3],constructor:27,discard:17,"0x014ae830":[],disabl:[27,28,19,4],"0x0138c2b0":[],absolut:[6,19,20,25,8,17,4],fro:17,from_int:[],"96014e":4,easy_instal:28,automat:[19,28,7,24,9,16,26,17,4,18],"871672518271819j":22,diagon:17,"23370055013617e":22,empti:[17,11],"46771150871022j":27,"56e":17,"72e":6,legendr:[7,2,13],"63448215208818e":16,"131967049321725588398296e":16,renorm:24,meissel:23,"536643565778565j":9,"0x0130ce30":[],log10:22,overflowerror:[25,8],"function":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],"0x0139cc70":[],"238410049439l":10,"707106781186548j":19,"86579517236206j":22,shank:[4,3],"519555750556794218804724e":24,triangular:4,"9219865355293e":6,yeah:[],"6141851416j":0,"0x013da5b0":[],uninstal:28,dirichletl:24,"1000000j":[9,0],overflow:[],highest:[],bug:[19,25,28,1],count:[23,6,19,17,2],made:[7,20],wise:17,whether:[19,7,1,10],wish:4,"455089860562227j":22,smooth:[6,7,20,4],displai:[22,25,19],troubl:7,"333332j":0,below:[19,7,24,10,0,4,18],limit:[5,21,13,22,14,15,7,9,25,10,11,0,3,16,23,4],"0x0133bb70":[],otherwis:[14,28,7,24,10,0,27],problem:[25,7,10,3,27,4,18],reliabl:27,block:19,reciproc:[22,6,23,11],evalu:[3,0,4,6,7,9,10,11,12,13,14,15,16,18,19,20,22,23,24,25,26,27],"int":[6,19,25,8,17,11],q_n:[],dure:[28,19,4],evalmath:[],asinh:21,"0x0134d970":[],implement:[6,11,12,13,22,14,15,7,24,9,25,19,10,2,0,16,17,23,4,18],evalf:10,hyperbol:[9,5,7,2,21],"2iz":[],inf:[6,19,21,13,22,14,15,7,8,24,9,25,1,16,11,26,0,17,23,4],dirichletetafunct:24,"480717210191852440616782e":16,probabl:[6,25,7,9,1,17,4],"0x01356970":[],"91682e":20,"47e":17,"0x0138c8b0":[],"243554598118700063281496e":16,percent:19,detail:[5,28,20,25,15,7,8,9,1,23,4],virtual:7,hurwitz:[2,24],other:[28,19,12,22,15,7,9,1,10,2,0,16,17,23,11,18],lookup:[10,24],futur:[25,1,8,20],branch:[6,13,22,14,9,0,11],"3937692045497259717762649j":13,"75977e":11,cplot:19,"0x01373070":[],"0412239966702e":16,repeat:[7,12,20],"97336609573659199632j":0,"8660254037844386467637232j":6,"class":[19,7,1,17],june:16,"164633059729968297147448e":16,jung:[],siegeltheta:24,"25e":24,debian:28,"100j":0,"56964379417266e":11,"45395195383789e":[],sphinx:[5,28],baker:20,rule:[7,20,3],"22311232304258e":11,"0x0139d070":[],richardson:[4,3],invari:[22,26]},titles:["Hypergeometric functions","Interval arithmetic","Mathematical functions","Numerical calculus","Sums, products, limits and extrapolation","Welcome to mpmath’s documentation!","Number-theoretical, combinatorial and integer functions","Numerical integration (quadrature)","Arithmetic and number parts","Exponential integrals and error functions","Number identification","Factorials and gamma functions","Polynomials","Orthogonal polynomials","Trigonometric functions","Elliptic functions","Bessel functions and related functions","Matrices","Ordinary differential equations","Mpmath basics","Function approximation","Hyperbolic functions","Powers and logarithms","Mathematical constants","Zeta functions, L-series and polylogarithms","Technical details","Differentiation","Root-finding and optimization","Setting up mpmath"],modules:{},descrefs:{"mpmath.functions":{hyper:[0,0],ellipe:[15,0],meijerg:[0,0],ellipk:[15,0],ci:[9,0],powm1:[22,0],zetazero:[24,0],acsch:[21,0],cospi:[14,0],acosh:[21,0],gammaprod:[11,0],grampoint:[24,0],altzeta:[24,0],ln:[22,0],csch:[21,0],rf:[11,0],li:[9,0],frexp:[8,0],trigamma:[11,0],degrees:[14,0],hermite:[13,0],jacobi:[13,0],euler:[23,2],psi:[11,0],legendre:[13,0],factorial:[11,0],bernoulli:[6,0],ceil:[8,0],catalan:[23,2],siegelz:[24,0],coth:[21,0],primepi2:[6,0],betainc:[11,0],radians:[14,0],hankel2:[16,0],primepi:[6,0],modf:[8,0],shi:[9,0],mertens:[23,2],stieltjes:[24,0],ei:[9,0],gegenbauer:[13,0],cyclotomic:[6,0],glaisher:[23,2],j0:[16,0],j1:[16,0],cosh:[21,0],airybi:[16,0],hypot:[8,0],sec:[14,0],arg:[8,0],superfac:[11,0],fresnels:[9,0],sincpi:[14,0],degree:[23,2],asin:[14,0],atan:[14,0],hyperfac:[11,0],barnesg:[11,0],re:[8,0],sinpi:[14,0],hankel1:[16,0],clsin:[24,0],appellf1:[0,0],besseli:[16,0],besselk:[16,0],besselj:[16,0],csc:[14,0],power:[22,0],legenq:[13,0],legenp:[13,0],bessely:[16,0],lambertw:[22,0],binomial:[11,0],sinh:[21,0],e1:[9,0],ker:[16,0],hypercomb:[0,0],expm1:[22,0],dirichlet:[24,0],cot:[14,0],polyexp:[24,0],erfc:[9,0],clcos:[24,0],asech:[21,0],acos:[14,0],digamma:[11,0],acot:[14,0],erfi:[9,0],hyp2f3:[0,0],hyp2f2:[0,0],hyp2f1:[0,0],hyp2f0:[0,0],ff:[11,0],bell:[6,0],cbrt:[22,0],harmonic:[11,0],ldexp:[8,0],bernfrac:[6,0],struveh:[16,0],zeta:[24,0],struvel:[16,0],kei:[16,0],log:[22,0],whitw:[0,0],chi:[9,0],airyai:[16,0],sinc:[14,0],whitm:[0,0],pi:[23,2],log10:[22,0],asinh:[21,0],polylog:[24,0],acoth:[21,0],hurwitz:[24,0],fresnelc:[9,0],twinprime:[23,2],cos:[14,0],laguerre:[13,0],gammainc:[9,0],bei:[16,0],tanh:[21,0],erfinv:[9,0],loggamma:[11,0],erf:[9,0],chebyt:[13,0],ber:[16,0],root:[22,0],coulombc:[16,0],coulombg:[16,0],coulombf:[16,0],apery:[23,2],unitroots:[22,0],im:[8,0],fibonacci:[6,0],tan:[14,0],conj:[8,0],fabs:[8,0],floor:[8,0],atanh:[21,0],sqrt:[22,0],fac2:[11,0],npdf:[9,0],sin:[14,0],ncdf:[9,0],phi:[23,2],primezeta:[24,0],expint:[9,0],bernpoly:[6,0],khinchin:[23,2],beta:[11,0],siegeltheta:[24,0],asec:[14,0],riemannr:[6,0],hyp0f1:[0,0],hyperu:[0,0],agm:[22,0],e:[23,2],chebyu:[13,0],sech:[21,0],hyp1f1:[0,0],hyp1f2:[0,0],atan2:[8,0],si:[9,0],gamma:[11,0],exp:[22,0],acsc:[14,0]},"mpmath.identification":{pslq:[10,0],findpoly:[10,0],identify:[10,0]},"mpmath.mptypes":{fmul:[8,0],fneg:[8,0],fdiv:[8,0],fsub:[8,0],fadd:[8,0]},"mpmath.quadrature.TanhSinh":{calc_nodes:[7,3],sum_next:[7,3]},"mpmath.linalg":{mnorm:[17,0],norm:[17,0]},"mpmath.elliptic":{djtheta:[15,0],jsn:[15,0],jdn:[15,0],jtheta:[15,0],jcn:[15,0]},"mpmath.odes":{odefun:[18,0]},"mpmath.quadrature.GaussLegendre":{calc_nodes:[7,3]},"mpmath.quadrature":{TanhSinh:[7,1],QuadratureRule:[7,1],GaussLegendre:[7,1]},mpmath:{rand:[19,0],fsum:[19,0],plot:[19,0],isnan:[19,0],monitor:[19,0],quadosc:[7,0],fraction:[19,0],nprint:[19,0],cplot:[19,0],isint:[19,0],almosteq:[19,0],linspace:[19,0],timing:[19,0],quad:[7,0],mpmathify:[19,0],nstr:[19,0],arange:[19,0],chop:[19,0],absmin:[19,0],fdot:[19,0],fprod:[19,0],isinf:[19,0],absmax:[19,0]},"mpmath.optimization":{MDNewton:[27,1],Newton:[27,1],ANewton:[27,1],MNewton:[27,1],Ridder:[27,1],Anderson:[27,1],Illinois:[27,1],findroot:[27,0],Pegasus:[27,1],Secant:[27,1],Bisection:[27,1],Muller:[27,1],Halley:[27,1]},"mpmath.quadrature.QuadratureRule":{guess_degree:[7,3],clear:[7,3],calc_nodes:[7,3],estimate_error:[7,3],sum_next:[7,3],summation:[7,3],get_nodes:[7,3],transform_nodes:[7,3]},"mpmath.calculus":{polyroots:[12,0],diffs:[26,0],taylor:[20,0],pade:[20,0],nsum:[4,0],chebyfit:[20,0],fsum:[4,0],nprod:[4,0],sumem:[4,0],fourierval:[20,0],limit:[4,0],polyval:[12,0],diff:[26,0],fprod:[4,0],richardson:[4,0],fourier:[20,0],shanks:[4,0],differint:[26,0]}},filenames:["functions/hypergeometric","intervals","functions/index","calculus/index","calculus/sums_limits","index","functions/numtheory","calculus/integration","functions/numberparts","functions/expintegrals","identification","functions/gamma","calculus/polynomials","functions/orthogonal","functions/trigonometric","functions/elliptic","functions/bessel","matrices","calculus/odes","basics","calculus/approximation","functions/hyperbolic","functions/powers","functions/constants","functions/zeta","technical","calculus/differentiation","calculus/optimization","setup"]})