Rule: Q[13, 28]

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.

• $P_1$:
  $\frac{1300075}{1024}\cdot t^{13}-\frac{2028117}{512}\cdot t^{11}+\frac{4849845}{1024}\cdot t^9-\frac{692835}{256}\cdot t^7+\frac{765765}{1024}\cdot t^5-\frac{45045}{512}\cdot t^3+\frac{3003}{1024}\cdot t$
• $P_2$:
  $\frac{1300075}{1024}\cdot t^{41}-\frac{7326079487692606077006153752602524655043397910117}{556887437614701325953658047096143814495872512}\cdot t^{39}+\frac{13851566936341366040979283165039434369884540764290105}{219204817631086809428508648788219608980937817536}\cdot t^{37}-\frac{7531017555990671395996707333033469572345247209835406673}{40333686444119972934845591377032408052492558426624}\cdot t^{35}+\frac{275742419606543768520594701345446743533077636986360838265}{726006355994159512827220644786583344944866051679232}\cdot t^{33}-\frac{1040564745968188605069663505091675236411419505212600644665}{1845266154818488761769185805499232668401534548018048}\cdot t^{31}+\frac{1479965505061746490452277244055183549932398181842078697566031}{2340720117387252994304212194275776639867346574160893888}\cdot t^{29}-\frac{2557833067348100268283993842261297300893513413931457766900595}{4681440234774505988608424388551553279734693148321787776}\cdot t^{27}+\frac{43662009515164483430594060677009324472311873614439993769490393}{118596485947620818378080084509972683086612226424151956992}\cdot t^{25}-\frac{501322812240352108687818340398710013628361913763295257869825}{2578184477122191703871306184999406154056787530959825152}\cdot t^{23}+\frac{882121514865972879627793489837082557907347867330686488910575}{10957284027769314741453051286247476154741347006579256896}\cdot t^{21}-\frac{59984446872794767300122237883897249030245019016066711520885}{2306796637425118892937484481315258137840283580332475136}\cdot t^{19}+\frac{82772248927168787713914902866391837011651457617589548916925}{12755228465762422113889620073154956762175685679485450752}\cdot t^{17}-\frac{624711909322505822152413096439690431512504440446974296224665}{507020331514056279027112397907909531296483505759546667392}\cdot t^{15}+\frac{632419513548556825941706141150003680386717668539864367946425}{3633645709184069999694305518340018307624798457943417782976}\cdot t^{13}-\frac{128732770629978116195369394600130184993741495103985158097675}{7267291418368139999388611036680036615249596915886835565952}\cdot t^{11}+\frac{1534427357018538425878655260725992587342874152086852958995}{1236985773339257872236359325392346657914825006959461372928}\cdot t^9-\frac{11352306716340235843888207598056791915751353116452515438675}{203484159714307919982881109027041025226988713644831395846656}\cdot t^7+\frac{2623095505803334808793620998366773953558529066044307165}{1816822854592034999847152759170009153812399228971708891488}\cdot t^5-\frac{512770572106198995841691421508004273781959438375413075}{29069165673472559997554444146720146460998387663547342263808}\cdot t^3+\frac{3745142811811765035824512173530351393203247813213775}{58138331346945119995108888293440292921996775327094684527616}\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.