Rule: Q[50]

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.

• $P_1$:
  $\frac{12611418068195524166851562157}{140737488355328}\cdot t^{50}-\frac{156050375086257748529223875175}{140737488355328}\cdot t^{48}+\frac{226836112238787036521861509275}{35184372088832}\cdot t^{46}-\frac{823773249709279237895181270525}{35184372088832}\cdot t^{44}+\frac{4189728463575151392735706892025}{70368744177664}\cdot t^{42}-\frac{7928255400303748020099876118755}{70368744177664}\cdot t^{40}+\frac{5790298887862287879848224131675}{35184372088832}\cdot t^{38}-\frac{6684039602901787158511168414725}{35184372088832}\cdot t^{36}+\frac{24770264410753681822717859419275}{140737488355328}\cdot t^{34}-\frac{18602568051449552212241926551825}{140737488355328}\cdot t^{32}+\frac{1423900270604780539702468452115}{17592186044416}\cdot t^{30}-\frac{712769410486857922635873160725}{17592186044416}\cdot t^{28}+\frac{583174972216520118520259858775}{35184372088832}\cdot t^{26}-\frac{194391657405506706173419952925}{35184372088832}\cdot t^{24}+\frac{26248579962778792027330678575}{17592186044416}\cdot t^{22}-\frac{5693353963757653481984400705}{17592186044416}\cdot t^{20}+\frac{7838675747202566388239392275}{140737488355328}\cdot t^{18}-\frac{1052956443654076082002306425}{140737488355328}\cdot t^{16}+\frac{26998883170617335435956575}{35184372088832}\cdot t^{14}-\frac{2052546673789621992207225}{35184372088832}\cdot t^{12}+\frac{222078820442811559812585}{70368744177664}\cdot t^{10}-\frac{8065816723104536070675}{70368744177664}\cdot t^8+\frac{90048990529077755175}{35184372088832}\cdot t^6-\frac{1067774591253886425}{35184372088832}\cdot t^4+\frac{20146690401016725}{140737488355328}\cdot t^2-\frac{15801325804719}{140737488355328}$

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.