Rule: Q[2, 3, 40]

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^{45}-\frac{3798738450570985823085951780981501473313}{227961392259805374529635366690340009766}\cdot t^{43}+\frac{2712870981854339293027912237252970937480}{31429892952763863930165673480561828589}\cdot t^{41}-\frac{78307453294562635246289673320824630454815}{282869036574874775371491061325056457301}\cdot t^{39}+\frac{9173146600073455622199425292964502995953655}{14897769259610071502898529229786306751186}\cdot t^{37}-\frac{35042918248600874282516205395874606036266023}{34761461605756833506763234869501382419434}\cdot t^{35}+\frac{2757153518707949367845273664609090748270337}{2190848420530892868073313122027398051645}\cdot t^{33}-\frac{165258203856675360081662725077257080235620}{134963657973633062758946715534177263941}\cdot t^{31}+\frac{4987154575078850395909408806622748277745717753}{5299078103018754943104524892018401914115483}\cdot t^{29}-\frac{10025094879758919279198826157939985832579602169}{17411256624204480527343438930917606289236587}\cdot t^{27}+\frac{1640332623926796717913526094724662926877762056748}{5832770969108500976660052041857398106894256645}\cdot t^{25}-\frac{127799386774157685524495952345345091509672270306}{1166554193821700195332010408371479621378851329}\cdot t^{23}+\frac{36082932225472754801526820586937583447569683945}{1065114698706769743564009503295698784737212083}\cdot t^{21}-\frac{25507053592326859412059838403358445143444406605}{3093904601005378778924027604811315517569997003}\cdot t^{19}+\frac{284485042198076835020569273634343285106604561790}{182540371459317347956517628683867615536629823177}\cdot t^{17}-\frac{287075056969561541203004449134428401955063084044}{1277782600215221435695623400787073308756408762239}\cdot t^{15}+\frac{8790042256012545199776410186777369572497836607}{365080742918634695913035257367735231073259646354}\cdot t^{13}-\frac{35828669280106389383699469546887111730078010995}{19349279374687638883390868640489967246882761256762}\cdot t^{11}+\frac{15989270467110752124778874543084834308687167620}{164468874684844930508822383444164721598503470682477}\cdot t^9-\frac{26087477482395685644010143039801686723834692935}{8058974859557401594932296788764071358326670063441373}\cdot t^7+\frac{6584272781850684067372894383817859257449372567}{108220519542627964274805128306260386811815283709069866}\cdot t^5-\frac{2790906354994559904550813617714377343108109}{5322320633243998243023203031455428859597472969298518}\cdot t^3+\frac{21018204962286838691250125554552810298732245}{16287188191165508623358171810092188215178200198215014833}\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.