Rule: Q[31]

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.

• $P_1$:
  $\frac{-1}{8222838654177922817725562880000000}\cdot t^{31}+\frac{31}{265252859812191058636308480000000}\cdot t^{30}-\frac{31}{589450799582646796969574400000}\cdot t^{29}+\frac{899}{60977668922342772100300800000}\cdot t^{28}-\frac{899}{311110555726238633164800000}\cdot t^{27}+\frac{899}{2133817254638125056000000}\cdot t^{26}-\frac{899}{18939206402113536000000}\cdot t^{25}+\frac{899}{212119111703671603200}\cdot t^{24}-\frac{899}{2946098773662105600}\cdot t^{23}+\frac{20677}{1152821259259084800}\cdot t^{22}-\frac{20677}{23818621059072000}\cdot t^{21}+\frac{20677}{594115264512000}\cdot t^{20}-\frac{20677}{17823457935360}\cdot t^{19}+\frac{392863}{12194997534720}\cdot t^{18}-\frac{392863}{526944337920}\cdot t^{17}+\frac{6678671}{464950886400}\cdot t^{16}-\frac{6678671}{29059430400}\cdot t^{15}+\frac{392863}{129153024}\cdot t^{14}-\frac{392863}{11860992}\cdot t^{13}+\frac{268801}{912384}\cdot t^{12}-\frac{268801}{126720}\cdot t^{11}+\frac{2956811}{241920}\cdot t^{10}-\frac{1344005}{24192}\cdot t^9+\frac{175305}{896}\cdot t^8-\frac{58435}{112}\cdot t^7+\frac{81809}{80}\cdot t^6-\frac{56637}{40}\cdot t^5+\frac{31465}{24}\cdot t^4-\frac{4495}{6}\cdot t^3+\frac{465}{2}\cdot t^2-31\cdot t+1$

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.