Rule: Q[4, 67]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{71}-\frac{11413941195521372823262207939244845321014765735618092129209063429}{606292823696970141042991036099731853364187003367180712859258}\cdot t^{69}+\frac{44311443951324199421744020298308988824788684651071676236133360918497}{4244049765878790987300937252698122973549309023570264990014806}\cdot t^{67}-\frac{20556665708979705679328149543641102211725839843122647246893642609794835}{5658733021171721316401249670264163964732412031427019986686408}\cdot t^{65}+\frac{629810255428766723572974941728969381210513550979777323151158310864803910}{707341627646465164550156208783020495591551503928377498335801}\cdot t^{63}-\frac{66149311614703432322172094583426422142526945636408620880979311198941024235}{404195215797980094028660690733154568909458002244787141906172}\cdot t^{61}+\frac{9477339397586860038014139427266505786335154475710844103503039361914420002755}{404195215797980094028660690733154568909458002244787141906172}\cdot t^{59}-\frac{4344692860007724151251330292674051533531351241019804596574850334221177374682205}{1616780863191920376114642762932618275637832008979148567624688}\cdot t^{57}+\frac{202809796322739252116147281833281796467914315930601791655890932796551933420670725}{808390431595960188057321381466309137818916004489574283812344}\cdot t^{55}-\frac{250046068333611600533092888659804134124721005709941580761984782164303140030113844525}{12934246905535363008917142103460946205102656071833188540997504}\cdot t^{53}+\frac{16056749927496176319199009745935293036809733731305735274850662029231831860640832740875}{12934246905535363008917142103460946205102656071833188540997504}\cdot t^{51}-\frac{3461247788674847873055321359726734309148523938478914973895703221300258775911352320395375}{51736987622141452035668568413843784820410624287332754163990016}\cdot t^{49}+\frac{39332393608706998525139359863532155976184875389832994558601144227283432656349824839534125}{12934246905535363008917142103460946205102656071833188540997504}\cdot t^{47}-\frac{12105152793905343564694248662089588895535234370979032896875628467398856209200672714378650625}{103473975244282904071337136827687569640821248574665508327980032}\cdot t^{45}+\frac{394966437792841864921447490075189634428162583501298740571687916288118763004081543434999423125}{103473975244282904071337136827687569640821248574665508327980032}\cdot t^{43}-\frac{43759425633421404739366194086726188606836202304838984128703713967522247385171164374496785579375}{413895900977131616285348547310750278563284994298662033311920128}\cdot t^{41}+\frac{64299587325739686980405538335193493809661748176380047018683503668969617557861978069336629431875}{25868493811070726017834284206921892410205312143666377081995008}\cdot t^{39}-\frac{328112898948494347509159004223142523783315354368274504890103124076058249813226843543467480240168125}{6622334415634105860565576756972004457012559908778592532990722048}\cdot t^{37}+\frac{5533645587779535839902254259964093439873038961751506375868340318084983359764249827021993863615984375}{6622334415634105860565576756972004457012559908778592532990722048}\cdot t^{35}-\frac{314878859857871587262516294825033983457359435004647616968499709682784773998930805308272577598221684375}{26489337662536423442262307027888017828050239635114370131962888192}\cdot t^{33}+\frac{470370340047199314040986965717397375125815961925202073175879605698321601253217916746081653807202134375}{3311167207817052930282788378486002228506279954389296266495361024}\cdot t^{31}-\frac{37582562024743211870418789243328985401973620456752371351701053737540891912129863168403067992231651803125}{26489337662536423442262307027888017828050239635114370131962888192}\cdot t^{29}+\frac{311705239378461882228694392589328221942950192281803417212885303725186904232490565516106661841592524103125}{26489337662536423442262307027888017828050239635114370131962888192}\cdot t^{27}-\frac{8521148253855484839634277667046630377317893433106875870185565510611343748149969280464987797687997160421875}{105957350650145693769049228111552071312200958540457480527851552768}\cdot t^{25}+\frac{23770482228061920763036467891785265114880476034249475521737876215629091561399942977581801060688479709921875}{52978675325072846884524614055776035656100479270228740263925776384}\cdot t^{23}-\frac{1712811057355848976213858671843205264561350288270479816966751468063877128070283613437517745915605578309953125}{847658805201165550152393824892416570497607668323659844222812422144}\cdot t^{21}+\frac{6142132325301425161730340349701494201713358763070825972709163301078934514472975629880321824572904491535796875}{847658805201165550152393824892416570497607668323659844222812422144}\cdot t^{19}-\frac{68993849204713402858215588874648880785191263444593673738399228214852620212977603258251624343319410469614234375}{3390635220804662200609575299569666281990430673294639376891249688576}\cdot t^{17}+\frac{37155559775416182040887938055732129589173312583501603023506209479254192531578730413178632896795160121512734375}{847658805201165550152393824892416570497607668323659844222812422144}\cdot t^{15}-\frac{478441313315249636461133647953514336317972624993676803158379717999413331331346383191587045541139112121095859375}{6781270441609324401219150599139332563980861346589278753782499377152}\cdot t^{13}+\frac{555943677075362784423387612420667143130611093341104259620307556273756000256944517320424401226301581811558671875}{6781270441609324401219150599139332563980861346589278753782499377152}\cdot t^{11}-\frac{1779372114313344842151930251727902563686095538924517168036400648757675718367405145812498084471536997704246640625}{27125081766437297604876602396557330255923445386357115015129997508608}\cdot t^9+\frac{915192961699936381591095598231947543444713280692748516610864108754766558334346140667284178774207270963660390625}{27125081766437297604876602396557330255923445386357115015129997508608}\cdot t^7-\frac{8680347077527607086623954722537852767678693976512536600182464870074942872365243861893099207306972512499727734375}{868002616525993523356051276689834568189550252363427680484159920275456}\cdot t^5+\frac{1217206706269694314165160303431452249307449971449128179292302687735362586161220165300162688431862041765623828125}{868002616525993523356051276689834568189550252363427680484159920275456}\cdot t^3-\frac{204411023007413090095357157940978307739502123313655820063227263397729803086260180455966527423279519345251953125}{3472010466103974093424205106759338272758201009453710721936639681101824}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.