Rule: Q[3, 36]

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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{39}-\frac{75649945733402547}{3108479462940686}\cdot t^{37}+\frac{124076547139063299417}{1134595003973350390}\cdot t^{35}-\frac{285123847474693168851}{947720532730680914}\cdot t^{33}+\frac{6176186535747916726038}{10898786126402830511}\cdot t^{31}-\frac{565407303715890287573922}{730218670468989644237}\cdot t^{29}+\frac{579257126668033522482774}{730218670468989644237}\cdot t^{27}-\frac{2268012178494027456954606}{3651093352344948221185}\cdot t^{25}+\frac{16731130682471656208787315}{44543338898608368298457}\cdot t^{23}-\frac{20108207809846574599396215}{114263347609473640417781}\cdot t^{21}+\frac{7282673225089771178054385}{114263347609473640417781}\cdot t^{19}-\frac{2022904381752673625012625}{114263347609473640417781}\cdot t^{17}+\frac{22523870046629786944248594}{6055957423302102942142393}\cdot t^{15}-\frac{3503403462302524350719730}{6055957423302102942142393}\cdot t^{13}+\frac{2737703044558246890646170}{42391701963114720594996751}\cdot t^{11}-\frac{9852270725891205453454470}{1992409992266391867964847297}\cdot t^9+\frac{138089956500983413921995}{569259997790397676561384942}\cdot t^7-\frac{65943957784180986081}{9648474538820299602735338}\cdot t^5+\frac{1549058235570684336118335}{17061291393776008764221268096682}\cdot t^3-\frac{91731379968595680885}{254646140205612071107780120846}\cdot t$

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.