Rule: Q[3, 74]

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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^{77}-\frac{16488119093099274189534770977640678783395073}{1436294107552088134616653523486475695754}\cdot t^{75}+\frac{7476706527526620343826255966332986285954465125}{957529405034725423077769015657650463836}\cdot t^{73}-\frac{1069838064276244650748931331904045160649951512175}{319176468344908474359256338552550154612}\cdot t^{71}+\frac{651117821050250696819646198104458423505779880877125}{638352936689816948718512677105100309224}\cdot t^{69}-\frac{598322661997281125052849247797695417434778297910894525}{2553411746759267794874050708420401236896}\cdot t^{67}+\frac{215806998925691078103437512463900558017763520441067089075}{5106823493518535589748101416840802473792}\cdot t^{65}-\frac{3921024656814275430176715717837935158915065850465148705625}{638352936689816948718512677105100309224}\cdot t^{63}+\frac{936025307310218053432321627101162686427245540689920940427625}{1276705873379633897437025354210200618448}\cdot t^{61}-\frac{744062115824196242211172057395913421109938512916497128516898125}{10213646987037071179496202833681604947584}\cdot t^{59}+\frac{124359526236006929478283290651314305043690233350228332747320339875}{20427293974074142358992405667363209895168}\cdot t^{57}-\frac{8807745410426010706141778521925989394627731794370392493700793602625}{20427293974074142358992405667363209895168}\cdot t^{55}+\frac{1063479342296685440378801942354508201640634549204997284951878065421875}{40854587948148284717984811334726419790336}\cdot t^{53}-\frac{219844040291268235844982464035583145727570505237611601747355979574008125}{163418351792593138871939245338905679161344}\cdot t^{51}+\frac{19510274037138566205022508448022389621560090693271344166661793345013421875}{326836703585186277743878490677811358322688}\cdot t^{49}-\frac{372381130335917994253588632858961758041442203327099982214111875584921634375}{163418351792593138871939245338905679161344}\cdot t^{47}+\frac{6120501899952775285167558191371189664684866656569284841896038474028034315625}{81709175896296569435969622669452839580672}\cdot t^{45}-\frac{11090336437877047231358381029741907955014566798289136623510164920488388958359375}{5229387257362980443902055850844981733163008}\cdot t^{43}+\frac{540542701449921775827991080040041766175263601313494373763056976865279669970890625}{10458774514725960887804111701689963466326016}\cdot t^{41}-\frac{276168521894567552043598269344577798214366544690956347498256498361083417823203125}{255092061334779533848880773211950328446976}\cdot t^{39}+\frac{9923504794113980977784805697652400407266920735986725061241195479683327696266984375}{510184122669559067697761546423900656893952}\cdot t^{37}-\frac{609863548329028566235043887020451123638150440011577392395194648088471507772832296875}{2040736490678236270791046185695602627575808}\cdot t^{35}+\frac{15964752344621925078095620842042511170870247047165367869956314264637832136025201953125}{4081472981356472541582092371391205255151616}\cdot t^{33}-\frac{44293081553164266068655157079048096472207568469789691887339610264968356546992217734375}{1020368245339118135395523092847801313787904}\cdot t^{31}+\frac{828751385807494149568440591084337166134985521179884727429773512293366083850634219921875}{2040736490678236270791046185695602627575808}\cdot t^{29}-\frac{51924107601297094637922420893987150404336873235613317578270541237664948063829992611765625}{16325891925425890166328369485564821020606464}\cdot t^{27}+\frac{675169089937281485818365703380332739703358674707647864046490434076163276829757615014984375}{32651783850851780332656738971129642041212928}\cdot t^{25}-\frac{3607570706983623300137659581621327494156497559636199671035158674688054193321168498728515625}{32651783850851780332656738971129642041212928}\cdot t^{23}+\frac{31301539729749244893748315821199667663258740680680586594071462751848941843207013941548046875}{65303567701703560665313477942259284082425856}\cdot t^{21}-\frac{434571122068500527128488523363958034372877032170769482325572466934894671884139905456056640625}{261214270806814242661253911769037136329703424}\cdot t^{19}+\frac{2370114718718157999760166818902500750959714539520933329331971577267234888008933150610562109375}{522428541613628485322507823538074272659406848}\cdot t^{17}-\frac{2482190884385785220199686059917257548509581285571881958705745908457722095918101308520466015625}{261214270806814242661253911769037136329703424}\cdot t^{15}+\frac{15519663531305721218460001424555280161030631578595200736813038978257544948054330989492998046875}{1044857083227256970645015647076148545318813696}\cdot t^{13}-\frac{278908133803325745573344465529812726661196752899089512080080095446395276132944855045331916015625}{16717713331636111530320250353218376725101019136}\cdot t^{11}+\frac{427630724876702410172632050786526722507640764034142281250683822403400989077865583115111552734375}{33435426663272223060640500706436753450202038272}\cdot t^9-\frac{207815928389740556246798831334616898281317235132513895202989667335992846436716022889090708984375}{33435426663272223060640500706436753450202038272}\cdot t^7+\frac{114162698991686592569475687987761697909244545111023526694949465170971357452809018436072361328125}{66870853326544446121281001412873506900404076544}\cdot t^5-\frac{57891589057310555312604715872250561344713893546710242083687364538349669090558751452346923828125}{267483413306177784485124005651494027601616306176}\cdot t^3+\frac{4268969296743775053506191781204781467974261494102604652120645104733531359129090836597919921875}{534966826612355568970248011302988055203232612352}\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.