Rule: Q[4, 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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{32}-\frac{15247097407655691}{433141800595430}\cdot t^{30}+\frac{488165058434990702999}{3802118725626684540}\cdot t^{28}-\frac{36788923128349286397}{131025394680117575}\cdot t^{26}+\frac{8661615909213698810613}{21110811590860543684}\cdot t^{24}-\frac{75839963826952664065311}{179441898522314621314}\cdot t^{22}+\frac{72058441303420823431557}{228380598119309518036}\cdot t^{20}-\frac{24407963855060895412992}{141235369889572991417}\cdot t^{18}+\frac{2888015013357219430347}{41539814673403821005}\cdot t^{16}-\frac{101843589697524079469571}{5001393686677820049002}\cdot t^{14}+\frac{249539989192471052756577}{58587754615368749145452}\cdot t^{12}-\frac{820174680302795236991}{1331539877622017026033}\cdot t^{10}+\frac{311684806278512230707}{5326159510488068104132}\cdot t^8-\frac{492915010796056351719}{146469386538421872863630}\cdot t^6+\frac{2426370419192361278583}{23845216128455080902198964}\cdot t^4-\frac{7261049137593557934}{5961304032113770225549741}\cdot t^2+\frac{47613382458118695}{19637236811668890154752088}$

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.