Rule: Q[6, 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.

• $P_1$:
  $\frac{231}{16}\cdot t^6-\frac{315}{16}\cdot t^4+\frac{105}{16}\cdot t^2-\frac{5}{16}$
• $P_2$:
  $\frac{231}{16}\cdot t^{25}-\frac{9195504511022816175}{106865715920001184}\cdot t^{23}+\frac{987082928693024544975}{4381494352720048544}\cdot t^{21}-\frac{252273465066682070140525}{740472545609688203936}\cdot t^{19}+\frac{9018052831903524345062775}{27397484187558463545632}\cdot t^{17}-\frac{20345210764902602421538905}{95891194656454622409712}\cdot t^{15}+\frac{1267247021747816083178175}{13698742093779231772816}\cdot t^{13}-\frac{28532539698419833307325}{1053749391829171674832}\cdot t^{11}+\frac{78999949902853566845775}{15279366181522989285064}\cdot t^9-\frac{1153819767362636203562425}{1894641406508850671347936}\cdot t^7+\frac{75783429233640444446625}{1894641406508850671347936}\cdot t^5-\frac{2287829422287644637875}{1894641406508850671347936}\cdot t^3+\frac{421002998964409617125}{39787469536685864098306656}\cdot t$

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.