Rule: Q[1, 8, 20]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^9-\frac{36}{17}\cdot t^7+\frac{126}{85}\cdot t^5-\frac{84}{221}\cdot t^3+\frac{63}{2431}\cdot t$
• $P_3$:
  $t^{29}-\frac{682558414238608172389654}{92781458854220952288753}\cdot t^{27}+\frac{1235076984455913464764835637}{50875166605064488838332895}\cdot t^{25}-\frac{6274778110955366419364978340}{132275433173167670979665527}\cdot t^{23}+\frac{5145785769977353334935412568255}{84328464200789459111949374887}\cdot t^{21}-\frac{26839559022558799556900199313530}{493923861747481117655703481481}\cdot t^{19}+\frac{12953315844422793876085017022935}{377706482512779678207302662309}\cdot t^{17}-\frac{5832092077666940743315564855656}{377706482512779678207302662309}\cdot t^{15}+\frac{3328059174455070175195070505}{675682437411054880513958251}\cdot t^{13}-\frac{90280562857112164099640217012570}{82775828359916100247123483455257}\cdot t^{11}+\frac{37685181462928676423105395620205}{233277334468854464332802544282997}\cdot t^9-\frac{3511154651762916540599658311340}{233277334468854464332802544282997}\cdot t^7+\frac{26503562133569432426375784753}{33325333495550637761828934897571}\cdot t^5-\frac{655265193818211709262899170}{33325333495550637761828934897571}\cdot t^3+\frac{110954755072281635287194645}{766482670397664668522065502644133}\cdot t$

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.