Rule: Q[2, 4, 15]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{21}-\frac{2053262169605}{264794067328}\cdot t^{19}+\frac{3862638680166099}{224280575026816}\cdot t^{17}-\frac{74679857934980325}{3476348912915648}\cdot t^{15}+\frac{33959764353233085}{2057430989276608}\cdot t^{13}-\frac{58030158032339441}{7201008462468128}\cdot t^{11}+\frac{4883897032652131}{1963911398854944}\cdot t^9-\frac{70231738677666241}{150566540578879040}\cdot t^7+\frac{1469429012067705}{30113308115775808}\cdot t^5-\frac{1005661252452623}{421586313620861312}\cdot t^3+\frac{222542486174801}{6323794704312919680}\cdot t$

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.