Rule: Q[2, 7, 10]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^9-\frac{151}{50}\cdot t^7+\frac{1281}{650}\cdot t^5-\frac{651}{1430}\cdot t^3+\frac{56}{2145}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{19}-\frac{59223261144133103007}{8719239124929410350}\cdot t^{17}+\frac{336441156077334773677}{26157717374788231050}\cdot t^{15}-\frac{161370425973044134409149}{12219141709676075664490}\cdot t^{13}+\frac{3618828931625441841999541}{453988111213349580457590}\cdot t^{11}-\frac{2484797910836626927503487}{866704575952758289964490}\cdot t^9+\frac{1430702432085456985697063}{2407512710979884138790250}\cdot t^7-\frac{22343098874047412337633}{343930387282840591255750}\cdot t^5+\frac{319974457119560256257}{103179116184852177376725}\cdot t^3-\frac{18130300172095676688}{447109503467692768632475}\cdot t$

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.