Rule: Q[11, 12]

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.

• $P_1$:
  $\frac{88179}{256}\cdot t^{11}-\frac{230945}{256}\cdot t^9+\frac{109395}{128}\cdot t^7-\frac{45045}{128}\cdot t^5+\frac{15015}{256}\cdot t^3-\frac{693}{256}\cdot t$
• $P_2$:
  $\frac{88179}{256}\cdot t^{23}-\frac{12651587}{6400}\cdot t^{21}+\frac{789222161}{160000}\cdot t^{19}-\frac{2441459691671}{348000000}\cdot t^{17}+\frac{2534636112998717}{404550000000}\cdot t^{15}-\frac{135276693963330437}{37083750000000}\cdot t^{13}+\frac{112286339079265435357}{80657156250000000}\cdot t^{11}-\frac{4503009063482496203}{13198443750000000}\cdot t^9+\frac{149818674831913373}{2932987500000000}\cdot t^7-\frac{12461832089366933}{2932987500000000}\cdot t^5+\frac{1435426957014869}{8798962500000000}\cdot t^3-\frac{27152552055083}{14664937500000000}\cdot t$

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.