Rule: Q[1, 2, 4, 8]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^7-\frac{77}{45}\cdot t^5+\frac{749}{891}\cdot t^3-\frac{31}{297}\cdot t$
• $P_4$:
  $t^{15}-\frac{646576627207}{164781456795}\cdot t^{13}+\frac{343884350900909}{55465438357197}\cdot t^{11}-\frac{36142899049575851}{7185295423545975}\cdot t^9+\frac{1577324700316391}{714327615206325}\cdot t^7-\frac{3801532399394821}{7540124827177875}\cdot t^5+\frac{2102662882898711}{40716674066760525}\cdot t^3-\frac{233879228435939}{149294471578121925}\cdot t$

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.