Rule: Q[5, 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.

• $P_1$:
  $\frac{-1}{120}\cdot t^5+\frac{5}{24}\cdot t^4-\frac{5}{3}\cdot t^3+5\cdot t^2-5\cdot t+1$
• $P_2$:
  $\frac{-1}{120}\cdot t^{17}+\frac{52446507051977349311}{27721953074260051080}\cdot t^{16}-\frac{1309222495970093703217}{6930488268565012770}\cdot t^{15}+\frac{15216524107080774855025}{1386097653713002554}\cdot t^{14}-\frac{1148051444007899591391725}{2772195307426005108}\cdot t^{13}+\frac{207872689497266409606928255}{19405367151982035756}\cdot t^{12}-\frac{316425934159802502334196710}{1617113929331836313}\cdot t^{11}+\frac{4142299804041087947398432930}{1617113929331836313}\cdot t^{10}-\frac{39031596457743393037641144950}{1617113929331836313}\cdot t^9+\frac{11459490388222753154204897850}{70309301275297231}\cdot t^8-\frac{1258894282051271458164984318720}{1617113929331836313}\cdot t^7+\frac{593730176502478721270475335040}{231016275618833759}\cdot t^6-\frac{1307043618557196527100628175520}{231016275618833759}\cdot t^5+\frac{1817225701238915643391074612000}{231016275618833759}\cdot t^4-\frac{1467342198446801939952056928000}{231016275618833759}\cdot t^3+\frac{598990923152942837031227116800}{231016275618833759}\cdot t^2-\frac{94974975213378886331777491200}{231016275618833759}\cdot t+\frac{2997042974599927483784505600}{231016275618833759}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Laguerre type can be downloaded here packed into a single file.