Rule: Q[2, 3, 6, 22]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^5-\frac{25}{14}\cdot t^3+\frac{3}{7}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{11}-\frac{2114365}{488852}\cdot t^9+\frac{2243043}{488852}\cdot t^7-\frac{1964259}{907868}\cdot t^5+\frac{386565}{907868}\cdot t^3-\frac{11007}{453934}\cdot t$
• $P_4$:
  $\frac{3}{2}\cdot t^{33}-\frac{1091440979681711949266504212092221591850539799353275489123549379392162943277}{84117781012297110491838099713215007234797347483436444745854392432879500164}\cdot t^{31}+\frac{11635957220154610263081919816100279133793721423295809518043933482652154526798205}{227370362076239089659438383524820164555657230247728710148044422746073288943292}\cdot t^{29}-\frac{449922355341614896684719778942452357282850624872887150397312626812954915548665660881}{3693290476385389652883087382785416342959818219528981303289759580875841468950363602}\cdot t^{27}+\frac{603965855509790655258138294774258723794435774381984069502694236579271638221876455077}{3093525356288616974209765500110861552222753722340514254037576401075491144932783188}\cdot t^{25}-\frac{16174277655464599575661475399837501946714706861353630665970112745823212266839598890705}{72697845872782498893929489252605246477234712475002084969883045425274041905920404918}\cdot t^{23}+\frac{23144748437051958362531005270963563421897167318855506622880250460461372956797930085}{124696133572525727090788146230883784695085270111495857581274520455015509272590746}\cdot t^{21}-\frac{9334774843432909818987334654827805226984040575623408086900146626508322406688543900625}{81194996689081752011401767217195470091456951595456874122207037747708670180638374324}\cdot t^{19}+\frac{2946540726207180877281105866177856249514897806320433937159936627388471178644023815}{55536933439864399460603123951570088981844700133691432368130668774082537743254702}\cdot t^{17}-\frac{1126295616583104281114155685210178877570330597725385900406586963524196132438032014985}{62090291585768398596954292577855359481702374749467021387570087689424277196958756836}\cdot t^{15}+\frac{10400486083774457409614479812024719181533320705388413010284932300750371661623194656315}{2297340788673430748087308825380648300822987865730279791340093244508698256287474002932}\cdot t^{13}-\frac{10191239010380356756345607815002304061065393054282373955092122353347746009426355486195}{12679553968255281244251108324697039660311490720472890386819360791807623068355866131567}\cdot t^{11}+\frac{163106240987400354353652521925943499768349624273414063350225225700857821082224583312075}{1673701123809697124241146298860009235161116775102421531060155624518606245022974329366844}\cdot t^9-\frac{81201864550519466101928863837839983797646832546507563511485597733500710160832392835}{10728853357754468745135553197820572020263569071169368788847151439221834903993425188249}\cdot t^7+\frac{6751669592360047029789204762173221180442579638119580036051984889366107488056470095}{19925013378686870526680313081666776609060913989314542036430424101411979107416361063891}\cdot t^5-\frac{574449286268733881171857537996532271387353828626921438594795043722293598497430255}{79700053514747482106721252326667106436243655957258168145721696405647916429665444255564}\cdot t^3+\frac{24000084121202117430494764251962242492787199148139994536477814775298404880860047}{518050347845858633693688140123336191835583763722178092947191026636711456792825387661166}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.