Rule: Q[1, 8, 10]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^9-\frac{36}{17}\cdot t^7+\frac{126}{85}\cdot t^5-\frac{84}{221}\cdot t^3+\frac{63}{2431}\cdot t$
• $P_3$:
  $t^{19}-\frac{1691}{357}\cdot t^{17}+\frac{479104}{50715}\cdot t^{15}-\frac{28532072}{2769039}\cdot t^{13}+\frac{7558572590}{1131684939}\cdot t^{11}-\frac{819725910886}{313270967205}\cdot t^9+\frac{20960573192}{34807885245}\cdot t^7-\frac{31726028896}{422667177975}\cdot t^5+\frac{1078323949}{253600306785}\cdot t^3-\frac{77583893}{1098934662735}\cdot t$

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.