Rule: Q[37]

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.

• $P_1$:
  $\frac{-1}{13763753091226345046315979581580902400000000}\cdot t^{37}+\frac{37}{371993326789901217467999448150835200000000}\cdot t^{36}-\frac{37}{574063775910341384981480629862400000000}\cdot t^{35}+\frac{37}{1405870471617162575464850522112000000}\cdot t^{34}-\frac{37}{4864603708017863582923358208000000}\cdot t^{33}+\frac{37}{22335186905499832795791360000000}\cdot t^{32}-\frac{37}{130870235774413082787840000000}\cdot t^{31}+\frac{1147}{29551343561964244500480000000}\cdot t^{30}-\frac{1147}{262678609439682173337600000}\cdot t^{29}+\frac{33263}{81520947757142743449600000}\cdot t^{28}-\frac{33263}{1039808007106412544000000}\cdot t^{27}+\frac{33263}{15689832754692096000000}\cdot t^{26}-\frac{33263}{278517741207552000000}\cdot t^{25}+\frac{33263}{5793169017117081600}\cdot t^{24}-\frac{33263}{140806191388262400}\cdot t^{23}+\frac{765049}{91830124818432000}\cdot t^{22}-\frac{765049}{3035706605568000}\cdot t^{21}+\frac{765049}{117022703616000}\cdot t^{20}-\frac{765049}{5266021662720}\cdot t^{19}+\frac{765049}{277159034880}\cdot t^{18}-\frac{765049}{17108582400}\cdot t^{17}+\frac{13005833}{21134131200}\cdot t^{16}-\frac{13005833}{1816214400}\cdot t^{15}+\frac{565471}{8072064}\cdot t^{14}-\frac{565471}{988416}\cdot t^{13}+\frac{7351123}{1900800}\cdot t^{12}-\frac{565471}{26400}\cdot t^{11}+\frac{6220181}{64800}\cdot t^{10}-\frac{6220181}{18144}\cdot t^9+\frac{214489}{224}\cdot t^8-\frac{214489}{105}\cdot t^7+\frac{48433}{15}\cdot t^6-\frac{145299}{40}\cdot t^5+\frac{22015}{8}\cdot t^4-1295\cdot t^3+333\cdot t^2-37\cdot t+1$

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.