Rule: Q[41]

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.

• $P_1$:
  $\frac{-1}{33452526613163807108170062053440751665152000000000}\cdot t^{41}+\frac{41}{815915283247897734345611269596115894272000000000}\cdot t^{40}-\frac{41}{1019894104059872167932014086995144867840000000}\cdot t^{39}+\frac{41}{2011625451794619660615412400384901120000000}\cdot t^{38}-\frac{41}{5572369672561273298103635458129920000000}\cdot t^{37}+\frac{1517}{753022928724496391635626413260800000000}\cdot t^{36}-\frac{1517}{3486217262613409220535307468800000000}\cdot t^{35}+\frac{1517}{19921241500648052688773185536000000}\cdot t^{34}-\frac{1517}{137863262980263340406734848000000}\cdot t^{33}+\frac{1517}{1139365809754242482700288000000}\cdot t^{32}-\frac{1517}{11126619235881274245120000000}\cdot t^{31}+\frac{47027}{3948155212732065054720000000}\cdot t^{30}-\frac{47027}{52642069503094200729600000}\cdot t^{29}+\frac{1363783}{23598169087593952051200000}\cdot t^{28}-\frac{1363783}{421395876564177715200000}\cdot t^{27}+\frac{1363783}{8670697048645632000000}\cdot t^{26}-\frac{1363783}{205223598784512000000}\cdot t^{25}+\frac{1363783}{5582081886938726400}\cdot t^{24}-\frac{1363783}{174440058966835200}\cdot t^{23}+\frac{31367009}{144102657407385600}\cdot t^{22}-\frac{31367009}{5954655264768000}\cdot t^{21}+\frac{31367009}{283555012608000}\cdot t^{20}-\frac{31367009}{15595525693440}\cdot t^{19}+\frac{25911877}{820817141760}\cdot t^{18}-\frac{25911877}{60801269760}\cdot t^{17}+\frac{440501909}{89413632000}\cdot t^{16}-\frac{440501909}{9081072000}\cdot t^{15}+\frac{440501909}{1089728640}\cdot t^{14}-\frac{440501909}{155675520}\cdot t^{13}+\frac{197466373}{11975040}\cdot t^{12}-\frac{197466373}{2494800}\cdot t^{11}+\frac{70068713}{226800}\cdot t^{10}-\frac{70068713}{72576}\cdot t^9+\frac{6369883}{2688}\cdot t^8-\frac{374699}{84}\cdot t^7+\frac{374699}{60}\cdot t^6-\frac{374699}{60}\cdot t^5+\frac{50635}{12}\cdot t^4-\frac{5330}{3}\cdot t^3+410\cdot t^2-41\cdot t+1$

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.