Rule: Q[4, 19]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{23}-\frac{78773570205}{3381024574}\cdot t^{21}+\frac{9405110609961}{175813277848}\cdot t^{19}-\frac{225413970227853}{3252545640188}\cdot t^{17}+\frac{6337990954094679}{113839097406580}\cdot t^{15}-\frac{23342273091342}{813136410047}\cdot t^{13}+\frac{73745497559067}{7756070372756}\cdot t^{11}-\frac{221435557932501}{112463020404962}\cdot t^9+\frac{107980305524487}{449852081619848}\cdot t^7-\frac{129872348385527}{8434726530372150}\cdot t^5+\frac{939848410523}{2249260408099240}\cdot t^3-\frac{22415950321}{7872411428347340}\cdot t$

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.