Rule: Q[3, 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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{21}-\frac{492974097}{38114128}\cdot t^{19}+\frac{1092720951}{38114128}\cdot t^{17}-\frac{62676676797}{1762778420}\cdot t^{15}+\frac{104814789093}{3878112524}\cdot t^{13}-\frac{239868945099}{18495613576}\cdot t^{11}+\frac{190151996979}{48761163064}\cdot t^9-\frac{17182210131}{24380581532}\cdot t^7+\frac{42668603943}{609514538300}\cdot t^5-\frac{107290416779}{33645202514160}\cdot t^3+\frac{479989951}{11215067504720}\cdot t$

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.