Rule: Q[39]

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.

• $P_1$:
  $\frac{-1}{20397882081197443358640281739902897356800000000}\cdot t^{39}+\frac{1}{13410836345297464404102749335899340800000000}\cdot t^{38}-\frac{1}{18574565575204244327012118193766400000000}\cdot t^{37}+\frac{37}{1506045857448992783271252826521600000000}\cdot t^{36}-\frac{37}{4648289683484545627380409958400000000}\cdot t^{35}+\frac{37}{18972610952998145417879224320000000}\cdot t^{34}-\frac{37}{98473759271616671719096320000000}\cdot t^{33}+\frac{37}{632981005419023601500160000000}\cdot t^{32}-\frac{37}{4945164104836121886720000000}\cdot t^{31}+\frac{1147}{1435692804629841838080000000}\cdot t^{30}-\frac{1147}{15952142273664909312000000}\cdot t^{29}+\frac{33263}{6050812586562551808000000}\cdot t^{28}-\frac{33263}{92614478365753344000000}\cdot t^{27}+\frac{33263}{1651561342599168000000}\cdot t^{26}-\frac{33263}{34203933130752000000}\cdot t^{25}+\frac{33263}{820894395138048000}\cdot t^{24}-\frac{33263}{22802622087168000}\cdot t^{23}+\frac{765049}{16854111977472000}\cdot t^{22}-\frac{765049}{626805817344000}\cdot t^{21}+\frac{765049}{27005239296000}\cdot t^{20}-\frac{765049}{1350261964800}\cdot t^{19}+\frac{14535931}{1492394803200}\cdot t^{18}-\frac{14535931}{101335449600}\cdot t^{17}+\frac{10743949}{5960908800}\cdot t^{16}-\frac{10743949}{558835200}\cdot t^{15}+\frac{10743949}{62092800}\cdot t^{14}-\frac{10743949}{8236800}\cdot t^{13}+\frac{139671337}{17107200}\cdot t^{12}-\frac{139671337}{3326400}\cdot t^{11}+\frac{52978783}{302400}\cdot t^{10}-\frac{52978783}{90720}\cdot t^9+\frac{1708993}{1120}\cdot t^8-\frac{1708993}{560}\cdot t^7+\frac{1087541}{240}\cdot t^6-\frac{191919}{40}\cdot t^5+\frac{27417}{8}\cdot t^4-\frac{9139}{6}\cdot t^3+\frac{741}{2}\cdot t^2-39\cdot t+1$

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.