Rule: Q[5, 22]

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.

• $P_1$:
  $\frac{63}{8}\cdot t^5-\frac{35}{4}\cdot t^3+\frac{15}{8}\cdot t$
• $P_2$:
  $\frac{63}{8}\cdot t^{27}-\frac{566849699789789}{10935824832456}\cdot t^{25}+\frac{10161549992211670325}{67074881609868876}\cdot t^{23}-\frac{1094734634456733180625}{4225717541421739188}\cdot t^{21}+\frac{261858003696446239225}{910806287123482632}\cdot t^{19}-\frac{2702153023549236384985}{12447685924020929304}\cdot t^{17}+\frac{1061462236133092419505}{9335764443015696978}\cdot t^{15}-\frac{4760174172170774180725}{115141094797193596062}\cdot t^{13}+\frac{127928939774368035875}{12447685924020929304}\cdot t^{11}-\frac{2334106173418924794175}{1381693137566323152744}\cdot t^9+\frac{2884198410387047994955}{16657078380660673563636}\cdot t^7-\frac{2070703556979659994145}{207023688445354085719476}\cdot t^5+\frac{97114360141529503175}{360621908904810342866184}\cdot t^3-\frac{195956138132076425}{90888448585765208364648}\cdot t$

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.