Rule: Q[6, 15]

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.

• $P_1$:
  $\frac{231}{16}\cdot t^6-\frac{315}{16}\cdot t^4+\frac{105}{16}\cdot t^2-\frac{5}{16}$
• $P_2$:
  $\frac{231}{16}\cdot t^{21}-\frac{5205313449}{70709920}\cdot t^{19}+\frac{14289790791591}{89448048800}\cdot t^{17}-\frac{53308908835107}{277288951280}\cdot t^{15}+\frac{1126298183287221}{8041379587120}\cdot t^{13}-\frac{254450630417893}{4020689793560}\cdot t^{11}+\frac{11958624144649}{685344851175}\cdot t^9-\frac{1164763374231093}{420344842054000}\cdot t^7+\frac{9423837253467}{42034484205400}\cdot t^5-\frac{1187724569941}{168137936821600}\cdot t^3+\frac{6211503831}{168137936821600}\cdot t$

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.