Rule: Q[2, 3, 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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^5-\frac{25}{14}\cdot t^3+\frac{3}{7}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{21}-\frac{2699938063962315}{340533575735962}\cdot t^{19}+\frac{64378204797177595}{3575602545227601}\cdot t^{17}-\frac{2708088644893246606}{117994883992510833}\cdot t^{15}+\frac{447913939828386925}{24883274855563509}\cdot t^{13}-\frac{45223754002229624159}{5051304795679392327}\cdot t^{11}+\frac{34785319911939687220}{12398657225758508439}\cdot t^9-\frac{732725560105787690}{1377628580639834271}\cdot t^7+\frac{17700439017954155671}{316854573547161882330}\cdot t^5-\frac{3615638031710110835}{1330789208898079905786}\cdot t^3+\frac{43695445400587591}{1108991007415066588155}\cdot t$

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.