Rule: Q[1, 2, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{25}-\frac{4304920607}{685653390}\cdot t^{23}+\frac{535516272071}{30854402550}\cdot t^{21}-\frac{57135203279}{2056960170}\cdot t^{19}+\frac{34407359525693}{1208806926570}\cdot t^{17}-\frac{11213406733991}{574920367515}\cdot t^{15}+\frac{2634095698720717}{290718065840085}\cdot t^{13}-\frac{316692035130031}{111814640707725}\cdot t^{11}+\frac{38855217475558}{67088784424635}\cdot t^9-\frac{33887938275433}{462167181591930}\cdot t^7+\frac{7220648427839}{1386501544775790}\cdot t^5-\frac{186639634254031}{1085630709559443570}\cdot t^3+\frac{491711610341}{291836212247162250}\cdot t$

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.