Rule: Q[4, 23]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{27}-\frac{33059314784135133}{1130189098886792}\cdot t^{25}+\frac{306994130657306013753}{3532406028570668396}\cdot t^{23}-\frac{2670462834723937761651}{17662030142853341980}\cdot t^{21}+\frac{7414434520177325114331}{43398131208153926008}\cdot t^{19}-\frac{12310351497689448174543}{93648598922858471912}\cdot t^{17}+\frac{1643857484252486307057}{23412149730714617978}\cdot t^{15}-\frac{3224317708935659072781}{123749934290920123598}\cdot t^{13}+\frac{114589456579827772365537}{17324990800728817303720}\cdot t^{11}-\frac{26937741216510478840629}{24254987121020344225208}\cdot t^9+\frac{1410359537420216114589}{12127493560510172112604}\cdot t^7-\frac{10684012949502674551263}{1557516672985520675604428}\cdot t^5+\frac{586677435255356621553}{3115033345971041351208856}\cdot t^3-\frac{119436372097909205319}{77875833649276033780221400}\cdot t$

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.