Rule: Q[1, 6, 16]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^7-\frac{21}{13}\cdot t^5+\frac{105}{143}\cdot t^3-\frac{35}{429}\cdot t$
• $P_3$:
  $t^{23}-\frac{5695479319283}{973235417571}\cdot t^{21}+\frac{332613072544398149}{22314017242262031}\cdot t^{19}-\frac{60434669839704081761}{2789252155282753875}\cdot t^{17}+\frac{1822577886905920640846}{92045321124330877875}\cdot t^{15}-\frac{5576903735421573562}{472027287817081425}\cdot t^{13}+\frac{198610075438798898}{42911571619734675}\cdot t^{11}-\frac{7838768636456247158}{6719952115650450105}\cdot t^9+\frac{9825341915024369299}{54590805970954914375}\cdot t^7-\frac{44745439665748799999}{2893312716460610461875}\cdot t^5+\frac{1067710391708808827}{1735987629876366277125}\cdot t^3-\frac{4195757732088601}{578662543292122092375}\cdot t$

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.