Rule: Q[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.

• $P_1$:
  $\frac{1}{371993326789901217467999448150835200000000}\cdot t^{36}-\frac{1}{287031887955170692490740314931200000000}\cdot t^{35}+\frac{1}{468623490539054191821616840704000000}\cdot t^{34}-\frac{1}{1216150927004465895730839552000000}\cdot t^{33}+\frac{1}{4467037381099966559158272000000}\cdot t^{32}-\frac{1}{21811705962402180464640000000}\cdot t^{31}+\frac{31}{4221620508852034928640000000}\cdot t^{30}-\frac{31}{32834826179960271667200000}\cdot t^{29}+\frac{899}{9057883084126971494400000}\cdot t^{28}-\frac{899}{103980800710641254400000}\cdot t^{27}+\frac{899}{1426348432244736000000}\cdot t^{26}-\frac{899}{23209811767296000000}\cdot t^{25}+\frac{899}{445628385932083200}\cdot t^{24}-\frac{899}{10057585099161600}\cdot t^{23}+\frac{20677}{6122008321228800}\cdot t^{22}-\frac{20677}{189731662848000}\cdot t^{21}+\frac{20677}{6883688448000}\cdot t^{20}-\frac{20677}{292556759040}\cdot t^{19}+\frac{392863}{277159034880}\cdot t^{18}-\frac{20677}{855429120}\cdot t^{17}+\frac{351509}{1006387200}\cdot t^{16}-\frac{351509}{82555200}\cdot t^{15}+\frac{351509}{8072064}\cdot t^{14}-\frac{15283}{41184}\cdot t^{13}+\frac{198679}{76032}\cdot t^{12}-\frac{198679}{13200}\cdot t^{11}+\frac{168113}{2400}\cdot t^{10}-\frac{168113}{648}\cdot t^9+\frac{168113}{224}\cdot t^8-\frac{11594}{7}\cdot t^7+\frac{40579}{15}\cdot t^6-\frac{15708}{5}\cdot t^5+\frac{19635}{8}\cdot t^4-1190\cdot t^3+315\cdot t^2-36\cdot t+1$

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.