Rule: Q[2, 6, 9]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{17}-\frac{254210989592309}{36656488650340}\cdot t^{15}+\frac{1854202443865275}{139294656871292}\cdot t^{13}-\frac{1613387760735757}{117864709660324}\cdot t^{11}+\frac{113900576146157429}{14047330396789524}\cdot t^9-\frac{2811372282650667}{1017922492520980}\cdot t^7+\frac{2374935978717729}{4682443465596508}\cdot t^5-\frac{2598365956055557}{60871765052754604}\cdot t^3+\frac{720075718862805}{669589415580300644}\cdot t$

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.