Rule: Q[6, 8, 15]

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.

• $P_1$:
  $\frac{231}{16}\cdot t^6-\frac{315}{16}\cdot t^4+\frac{105}{16}\cdot t^2-\frac{5}{16}$
• $P_2$:
  $\frac{231}{16}\cdot t^{14}-\frac{3731}{80}\cdot t^{12}+\frac{1182181}{20400}\cdot t^{10}-\frac{200960617}{5814000}\cdot t^8+\frac{14859361517}{1482570000}\cdot t^6-\frac{123220867}{98838000}\cdot t^4+\frac{4422019}{98838000}\cdot t^2-\frac{22771}{889542000}$
• $P_3$:
  $\frac{231}{16}\cdot t^{29}-\frac{144932622283605439795318253215164707033394199253786365872972601}{1442118343571075730762921627993736939348362967718291132717920}\cdot t^{27}+\frac{939082652669761591962541108355123631217610371318635170439702082529}{3015469456407119353025269124134903940177426965498946758513170720}\cdot t^{25}-\frac{942670797982756272057648392983144757595023054851599551555470162315823}{1665104540459806217748640794483242269466722952511449663216491456950}\cdot t^{23}+\frac{2275188269150345477733179947283404407939640690291941841114781679500240759}{3396813262538004684207227220745814229712114823123357312961642572178000}\cdot t^{21}-\frac{30616507739381909336493986058819952895940006587509091484933240868048876049}{56613554375633411403453787012430237161868580385389288549360709536300000}\cdot t^{19}+\frac{1509002602307042310759519570334861994660610692570715171928984337578552783}{4966101261020474684513490088809669926479700033806077942926378029500000}\cdot t^{17}-\frac{131861662026328139294389717158198056119075583564207569387322687917660687}{1108673514652127166268009476357747029650734071128463291626924749103125}\cdot t^{15}+\frac{3211313978800351860542335918331580941956097555149079305101371784242781731}{100519731995126196408299525856435730688333222448980671774174510585350000}\cdot t^{13}-\frac{10309672116852609690207095316839892805586546104769517402476498824061756383}{1809355175912271535349391465415843152389998004081652091935141190536300000}\cdot t^{11}+\frac{3457723627346199260935960624766298575720400233496520703880418060063448431}{5428065527736814606048174396247529457169994012244956275805423571608900000}\cdot t^9-\frac{38111107180676339726683199723705598076067326501607989583822555426781941}{942372487454308091327808054904084975203123960459193797882886036737656250}\cdot t^7+\frac{107818729098882796691538858272024478330388956654345720512058773552257}{88693881172170173301440758108619762372058725690277063330153979928250000}\cdot t^5-\frac{1979151827732355072244679860389679463298887768022348669685328671227797}{171888741711665795858192189214505099477049810387756948733838413100948500000}\cdot t^3+\frac{6129340402792864594608402981132720529223374528791741729054922128173}{974036203032772843196422405548862230369948925530622709491751007572041500000}\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.