Rule: Q[8, 55]

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.

• $P_1$:
  $256\cdot t^8-3584\cdot t^6+13440\cdot t^4-13440\cdot t^2+1680$
• $P_2$:
  $256\cdot t^{63}-\frac{13033751947039591710842082174182198218235183970367388868603884383365072704}{59088519169067621599684761229441331372581320685129788196917730702075}\cdot t^{61}+\frac{5242240281059304918316783897940409982614505878371204613644769137184079520736}{59088519169067621599684761229441331372581320685129788196917730702075}\cdot t^{59}-\frac{261829517084650580139162453696159922682893168753873529874312745023751881680736}{11817703833813524319936952245888266274516264137025957639383546140415}\cdot t^{57}+\frac{2141200242038968852374651713267992631884418688118780159838178784664680965792422784}{555432080189235643037036755556748514902264414440220009051026668599505}\cdot t^{55}-\frac{276126988884173499407115809719900743169256918356335958235274921404076817995920734788}{555432080189235643037036755556748514902264414440220009051026668599505}\cdot t^{53}+\frac{5482198435085881565715577089622293877772926650159527961876739205061055812429251827398}{111086416037847128607407351111349702980452882888044001810205333719901}\cdot t^{51}-\frac{429532778061847434667630117482959383635174324392387282451879100792567136210034098701344}{111086416037847128607407351111349702980452882888044001810205333719901}\cdot t^{49}+\frac{27023150558818869523499420972841968977168477147280160698075743098541363303087572779813415}{111086416037847128607407351111349702980452882888044001810205333719901}\cdot t^{47}-\frac{117590028668036023119516451658977992880152340922018069244836273880554471689037758200373845}{9454163067050819455949561796710613019613011309620766111506836912332}\cdot t^{45}+\frac{9855031080040201247962050454807049083013530745051005961879040785907406855978124206138512255}{18908326134101638911899123593421226039226022619241532223013673824664}\cdot t^{43}-\frac{340382270181901252245639471682766087019366852051623443704824275074553426329519992324134066845}{18908326134101638911899123593421226039226022619241532223013673824664}\cdot t^{41}+\frac{9724236989349487588646753170759896199255038714444398263479347897171811849167025045233384701905}{18908326134101638911899123593421226039226022619241532223013673824664}\cdot t^{39}-\frac{1841455342953920351243674904475507789993336159449423087643376345489352655625178252366126748182475}{151266609072813111295192988747369808313808180953932257784109390597312}\cdot t^{37}+\frac{72243323561204440308305510709084897684747111021760085044222118147127537963705818643686298456433725}{302533218145626222590385977494739616627616361907864515568218781194624}\cdot t^{35}-\frac{586407682751941510397257871489764163509085903972596190758290927842661118013004150015058731953166225}{151266609072813111295192988747369808313808180953932257784109390597312}\cdot t^{33}+\frac{31429876043726289206216508399499801400761451286022227246049298336425344958821441916865849423301617925}{605066436291252445180771954989479233255232723815729031136437562389248}\cdot t^{31}-\frac{1384661998333861451322603844730564900905629738992953743350726448387454455969181807919020639736464637175}{2420265745165009780723087819957916933020930895262916124545750249556992}\cdot t^{29}+\frac{24929899079386707381392754213704672773026038817908628069686133675761194729928977073371620775742184610125}{4840531490330019561446175639915833866041861790525832249091500499113984}\cdot t^{27}-\frac{182089361392188714133695666033341623619767289310675222870005663119241470050289210001427302292557162405625}{4840531490330019561446175639915833866041861790525832249091500499113984}\cdot t^{25}+\frac{534551581707875340183936071955094518433621182419072106937617128782429356661632780522665027063283678620625}{2420265745165009780723087819957916933020930895262916124545750249556992}\cdot t^{23}-\frac{39895748112248222480819537868978507833880568508273716765453289678386544671308432591250348425256898661170625}{38724251922640156491569405119326670928334894324206657992732003992911872}\cdot t^{21}+\frac{291372791863457340286504500604287553308148083357328280665976875361709065843410916578092963208182054061299375}{77448503845280312983138810238653341856669788648413315985464007985823744}\cdot t^{19}-\frac{204373106780707519645775506127436689065429792836905170752600297593022633827451884830258684817932220695546875}{19362125961320078245784702559663335464167447162103328996366001996455936}\cdot t^{17}+\frac{3440472874580129688789692855014381375905600464573021640553311796943611182240778315224562055098097950389009375}{154897007690560625966277620477306683713339577296826631970928015971647488}\cdot t^{15}-\frac{21042953272370771358371803243839017818956591269010561976478481002249895464521054793161992154801184449130559375}{619588030762242503865110481909226734853358309187306527883712063886589952}\cdot t^{13}+\frac{44815021655985573888175974825297652559553840458832364084454724121141423665414082273681045998673862029190488125}{1239176061524485007730220963818453469706716618374613055767424127773179904}\cdot t^{11}-\frac{31339232059946579295499564543190353005348649016691024435227733427385860588312281147697561278687146774972236875}{1239176061524485007730220963818453469706716618374613055767424127773179904}\cdot t^9+\frac{13241811268901097696198612384904213019305115812968767709287185819546433699058878064193394069133329802721715625}{1239176061524485007730220963818453469706716618374613055767424127773179904}\cdot t^7-\frac{23955044338674042390903969763221746184153961095035305259995985646779372146541060630059213740363791842046090625}{9913408492195880061841767710547627757653732946996904446139393022185439232}\cdot t^5+\frac{4844846093644958118700695677551590455457804346061496377184576013904719717065855779336311731939027785915034375}{19826816984391760123683535421095255515307465893993808892278786044370878464}\cdot t^3-\frac{79783146076372832909978303795926020652702849443682063851838881582351336037167928362261018198416926954640625}{9913408492195880061841767710547627757653732946996904446139393022185439232}\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.