Rule: Q[12, 13]

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.

• $P_1$:
  $\frac{676039}{1024}\cdot t^{12}-\frac{969969}{512}\cdot t^{10}+\frac{2078505}{1024}\cdot t^8-\frac{255255}{256}\cdot t^6+\frac{225225}{1024}\cdot t^4-\frac{9009}{512}\cdot t^2+\frac{231}{1024}$
• $P_2$:
  $\frac{676039}{1024}\cdot t^{25}-\frac{113897875}{27648}\cdot t^{23}+\frac{122428248475}{10824192}\cdot t^{21}-\frac{162762848091025}{9059848704}\cdot t^{19}+\frac{91911271910897075}{5034353347584}\cdot t^{17}-\frac{52228553975713777025}{4213753751927808}\cdot t^{15}+\frac{5391794000036513461625275}{946094114590029073152}\cdot t^{13}-\frac{201966691589935661524681}{114678074495761099776}\cdot t^{11}+\frac{13591251201800897201395}{38226024831920366592}\cdot t^9-\frac{636076610214703187075}{14334759311970137472}\cdot t^7+\frac{59273215415530548341}{19113012415960183296}\cdot t^5-\frac{3842874456522219755}{38226024831920366592}\cdot t^3+\frac{110677163924317627}{114678074495761099776}\cdot t$

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.