Rule: Q[1, 2, 36]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{39}-\frac{75649945733402547}{7771198657351715}\cdot t^{37}+\frac{124076547139063299417}{2836487509933375975}\cdot t^{35}-\frac{285123847474693168851}{2369301331826702285}\cdot t^{33}+\frac{12352373071495833452076}{54493930632014152555}\cdot t^{31}-\frac{1130814607431780575147844}{3651093352344948221185}\cdot t^{29}+\frac{1158514253336067044965548}{3651093352344948221185}\cdot t^{27}-\frac{4536024356988054913909212}{18255466761724741105925}\cdot t^{25}+\frac{6692452272988662483514926}{44543338898608368298457}\cdot t^{23}-\frac{8043283123938629839758486}{114263347609473640417781}\cdot t^{21}+\frac{2913069290035908471221754}{114263347609473640417781}\cdot t^{19}-\frac{809161752701069450005050}{114263347609473640417781}\cdot t^{17}+\frac{45047740093259573888497188}{30279787116510514710711965}\cdot t^{15}-\frac{1401361384921009740287892}{6055957423302102942142393}\cdot t^{13}+\frac{1095081217823298756258468}{42391701963114720594996751}\cdot t^{11}-\frac{3940908290356482181381788}{1992409992266391867964847297}\cdot t^9+\frac{27617991300196682784399}{284629998895198838280692471}\cdot t^7-\frac{65943957784180986081}{24121186347050749006838345}\cdot t^5+\frac{309811647114136867223667}{8530645696888004382110634048341}\cdot t^3-\frac{18346275993719136177}{127323070102806035553890060423}\cdot t$

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.