Rule: Q[2, 4, 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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{22}-\frac{21703940836137923}{2794208237943850}\cdot t^{20}+\frac{42027029201559237}{2431716358426810}\cdot t^{18}-\frac{262592289065984469}{12158581792134050}\cdot t^{16}+\frac{662392414045240323}{39845409473079301}\cdot t^{14}-\frac{3613046556074683491}{444429567199730665}\cdot t^{12}+\frac{577469291852421331}{229877362344688275}\cdot t^{10}-\frac{1047921046375098841}{2222147835998653325}\cdot t^8+\frac{25219697121887517513}{511094002279690264750}\cdot t^6-\frac{345233232267838651}{143106320638313274130}\cdot t^4+\frac{76767549244621411}{2146594809574699111950}\cdot t^2-\frac{2147720438279}{511094002279690264750}$

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.