Rule: Q[3, 4, 44]

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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^7-\frac{77}{18}\cdot t^5+\frac{3745}{1782}\cdot t^3-\frac{155}{594}\cdot t$
• $P_3$:
  $\frac{5}{2}\cdot t^{51}-\frac{87157768709928771194357939184929783610143786534267915126581749199354139}{2690727698521596296935171052557073291089951689799433655268138047981726}\cdot t^{49}+\frac{43267204038346311571647579019817530963520159893546384094953455286976197245169}{218832847629213644435292058947887935154409136003853240032474765235281802991}\cdot t^{47}-\frac{32254554130744025923439259821001714782454802675081033356644577889772318027359363}{42672405287696660664881951494838147355109781520751381806332579220879951583245}\cdot t^{45}+\frac{15571441737448625434794346201765954963375263236063292914842930365310283427679166}{7672412263848490503382815521294131544656102132013884809623433435673365032139}\cdot t^{43}-\frac{7359302217867218133121574426394387966089926209021165004717099630041362994085946}{1808942728874847354456110976565283047114040340068314304707963980768516958797}\cdot t^{41}+\frac{3546553875491207850863028171877051766588247707449289702542365180148503128734453}{561396019305987110003620647899570600828495277952235473874885373341953538937}\cdot t^{39}-\frac{14192910512446349295969423454870673329588580235487087446802157615806179362325527}{1823590038420392677164257624148807606199983986546600250495073000855711428099}\cdot t^{37}+\frac{1268471029082309045353506992530806553219635026721248771918608772315274175984500247}{164123103457835340944783186173392684557998558789194022544556570077014028528910}\cdot t^{35}-\frac{3740702705370324148531084593005615739868063705028667947887807854242272629893809163}{598418084915491935444824848047601019080702437431368974508613955511574227097718}\cdot t^{33}+\frac{5373083201101975705561816241973815997582596213144411555928462991425246933545947198}{1296572517316899193463787170769802208008188614434632778101996903608410825378389}\cdot t^{31}-\frac{1417278446093272873149120108146613810640474505772937287577398461018629829246721982}{627373798701725416192155082630549455487833200532886828113869469487940721957285}\cdot t^{29}+\frac{4799751532702715393098438106301104475040187307526532060754511552689927110828362888}{4737753859161305729175240106761735543166740376438007426101290131650310969263635}\cdot t^{27}-\frac{19658568705338217890536882387459028077056106865860370232601964206436238655015980232}{52709198917449854337405449051010191726684105897408601136539994199699328589670925}\cdot t^{25}+\frac{1025031479584503678543521489183322060305320139942293071613523123318956389218571086}{9136261145691308085150277835508433232625245022217490863666932327947883622209627}\cdot t^{23}-\frac{13710359233365252366378039708417414068863587710953877402460198106844741665493660846}{500833224622896252304147048619235021752092977127013362799196381250233984017491371}\cdot t^{21}+\frac{23271377079655981912440393006389403331774951210116874615802286512670252757211776883}{4340554613398434186635941088033370188518139135100782477593035304168694528151591882}\cdot t^{19}-\frac{3606589257185133176097220949018082877795876377285020906759294767126476548529246755}{4340554613398434186635941088033370188518139135100782477593035304168694528151591882}\cdot t^{17}+\frac{198543610937890716967931816624744863712501779513662268587288052277734059569283066869}{1985803735629783640385943047775266861247048654308607983498813651657177746629353286015}\cdot t^{15}-\frac{71125757156588933150984482496431809800691441247881434364255326897370770860092350633}{7810828026810482318851375987916049654238391373613858068428667029851565803408789591659}\cdot t^{13}+\frac{292511554677141866221212020799161428617757984562640069104798265361061867865112414}{482358827224482656743801117346928310175068589703130996641857010510876761423944752681}\cdot t^{11}-\frac{2890779432750129104819915259917384709511883105566212976397164074008457644300643550}{102742430198814805886429637994895730067289609606766902284715543238816750183300232321053}\cdot t^9+\frac{39437595548340037728534014189422904662463831808635840326070841896721884303310757}{46541442739634057367357015501961313620225207770586716419571998219293057775341130880477}\cdot t^7-\frac{4979948976621184528563777067019762877364265697520823746570317926635234836928189}{336132642008468192097578445291942820590515389454237396363575542694894306155241500803445}\cdot t^5+\frac{4919343983943102954468925253149049590545009521558149302125725159088398397675803}{39932557870606021221192319300682807086153228267163402687992774472153443571242690295449266}\cdot t^3-\frac{4099417174662853911847807282507809633367099946261884062700565068421535260777}{13310852623535340407064106433560935695384409422387800895997591490717814523747563431816422}\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.