Rule: Q[10, 12]

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.

• $P_1$:
  $\frac{46189}{256}\cdot t^{10}-\frac{109395}{256}\cdot t^8+\frac{45045}{128}\cdot t^6-\frac{15015}{128}\cdot t^4+\frac{3465}{256}\cdot t^2-\frac{63}{256}$
• $P_2$:
  $\frac{46189}{256}\cdot t^{22}-\frac{5564559}{5888}\cdot t^{20}+\frac{7182734559}{3385600}\cdot t^{18}-\frac{1868043574397}{700819200}\cdot t^{16}+\frac{3999135573000799}{1947693360000}\cdot t^{14}-\frac{1386904017410797067}{1388705365680000}\cdot t^{12}+\frac{6564262289282082838453}{21559650802182000000}\cdot t^{10}-\frac{26732588628921841237}{479103351159600000}\cdot t^8+\frac{185727472669565827}{33041610424800000}\cdot t^6-\frac{746786462661752513}{2874620106957600000}\cdot t^4+\frac{3403953492432493}{958206702319200000}\cdot t^2-\frac{1772896747853}{4791033511596000000}$

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.