Rule: Q[2, 4, 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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{28}-\frac{19832197362872655617}{1912944396638492910}\cdot t^{26}+\frac{175120679183668928584615}{5475420746498358256293}\cdot t^{24}-\frac{1907976344884904719830613}{32852524478990149537758}\cdot t^{22}+\frac{210743204806119261464045}{3057702494797784480787}\cdot t^{20}-\frac{8107679068046607597340}{144486134022330960867}\cdot t^{18}+\frac{422415800548244324142343}{13196400240706227759186}\cdot t^{16}-\frac{1044445915916259597103765}{81377801484355071181647}\cdot t^{14}+\frac{1745254426919519122863451}{488266808906130427089882}\cdot t^{12}-\frac{2298018616944542202084205}{3417867662342912989629174}\cdot t^{10}+\frac{1436029993671366972927490}{17658982922105050446417399}\cdot t^8-\frac{2555874324399912666798713}{438951861206611253953803918}\cdot t^6+\frac{4637576593995795072389780}{21728117129727257070713293941}\cdot t^4-\frac{108001983857528840671103}{36213528549545428451188823235}\cdot t^2+\frac{282484052687588353627}{43456234259454514141426587882}$

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.