Rule: Q[2, 4, 13]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{19}-\frac{6523706162613}{947242382590}\cdot t^{17}+\frac{1271968937263439}{96145101832885}\cdot t^{15}-\frac{340906484373145}{24723026185599}\cdot t^{13}+\frac{1742580135265346}{206025218213325}\cdot t^{11}-\frac{382983832651706}{123615130927995}\cdot t^9+\frac{100441415714497}{152857419964725}\cdot t^7-\frac{117353462093153}{1579526672968825}\cdot t^5+\frac{204124551917}{54155200216074}\cdot t^3-\frac{3740307548549}{66340120264690650}\cdot t$

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.