Rule: Q[1, 2, 18]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{21}-\frac{492974097}{95285320}\cdot t^{19}+\frac{1092720951}{95285320}\cdot t^{17}-\frac{62676676797}{4406946050}\cdot t^{15}+\frac{104814789093}{9695281310}\cdot t^{13}-\frac{239868945099}{46239033940}\cdot t^{11}+\frac{190151996979}{121902907660}\cdot t^9-\frac{17182210131}{60951453830}\cdot t^7+\frac{42668603943}{1523786345750}\cdot t^5-\frac{107290416779}{84113006285400}\cdot t^3+\frac{479989951}{28037668761800}\cdot t$

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.