Rule: Q[2, 3, 22]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^5-\frac{25}{14}\cdot t^3+\frac{3}{7}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{27}-\frac{25780551264439426689}{2463357089651350900}\cdot t^{25}+\frac{28531476502037844803}{876156197292210212}\cdot t^{23}-\frac{86890513642061023191869}{1458800068491530002980}\cdot t^{21}+\frac{42451550984625626853581}{597413361382245620268}\cdot t^{19}-\frac{118368312078136961423297}{2041162318056005869249}\cdot t^{17}+\frac{2021921716254952262813513}{61234869541680176077470}\cdot t^{15}-\frac{283386776449210543179103}{21578001648020633474918}\cdot t^{13}+\frac{1357488952200127747899041}{377615028840361085811065}\cdot t^{11}-\frac{4156628943981175835171141}{6343932484518066241625892}\cdot t^9+\frac{158633137582788197290533}{2114644161506022080541964}\cdot t^7-\frac{6623149570564835818490747}{1357903643709938464576589740}\cdot t^5+\frac{1092273180186533512469419}{7332679676033667708713584596}\cdot t^3-\frac{41649512135367462237091}{30552831983473615452973269150}\cdot t$

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.