Rule: Q[1, 40]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{41}-\frac{820}{81}\cdot t^{39}+\frac{101270}{2133}\cdot t^{37}-\frac{7493980}{54747}\cdot t^{35}+\frac{6369883}{23463}\cdot t^{33}-\frac{101918128}{259515}\cdot t^{31}+\frac{1579730984}{3685113}\cdot t^{29}-\frac{91624397072}{254272797}\cdot t^{27}+\frac{148889645242}{630973237}\cdot t^{25}-\frac{229060992680}{1892919711}\cdot t^{23}+\frac{251967091948}{5184953991}\cdot t^{21}-\frac{229060992680}{15061056831}\cdot t^{19}+\frac{1088039715230}{296200784343}\cdot t^{17}-\frac{599082596240}{888602353029}\cdot t^{15}+\frac{299541298120}{3258208627773}\cdot t^{13}-\frac{1557614750224}{172685057271969}\cdot t^{11}+\frac{28632624085}{47095924710537}\cdot t^9-\frac{6737088020}{256411145646257}\cdot t^7+\frac{3368544010}{5164853076588891}\cdot t^5-\frac{354583580}{46483677689300019}\cdot t^3+\frac{17729179}{666266046879966939}\cdot t$

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.