Rule: Q[7, 12]

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.

• $P_1$:
  $\frac{-1}{5040}\cdot t^7+\frac{7}{720}\cdot t^6-\frac{7}{40}\cdot t^5+\frac{35}{24}\cdot t^4-\frac{35}{6}\cdot t^3+\frac{21}{2}\cdot t^2-7\cdot t+1$
• $P_2$:
  $\frac{-1}{5040}\cdot t^{19}+\frac{2527553045506323330569}{47692466235470083411440}\cdot t^{18}-\frac{10407790373332594419102}{1655988410953822340675}\cdot t^{17}+\frac{207377734977421796012343}{473139545986806383050}\cdot t^{16}-\frac{265922851964044152647243697}{13247907287630578725400}\cdot t^{15}+\frac{338415925128361719078993645}{529916291505223149016}\cdot t^{14}-\frac{3859469563705537725777816655}{264958145752611574508}\cdot t^{13}+\frac{64226324033944324589722988377}{264958145752611574508}\cdot t^{12}-\frac{196575219858214367848417932207}{66239536438152893627}\cdot t^{11}+\frac{1772865954965195487624743065671}{66239536438152893627}\cdot t^{10}-\frac{11722956958789804973477128792830}{66239536438152893627}\cdot t^9+\frac{8032176351772568654591013947910}{9462790919736127661}\cdot t^8-\frac{192190181937354330159367216479024}{66239536438152893627}\cdot t^7+\frac{65168144102636454063177435256848}{9462790919736127661}\cdot t^6-\frac{103442994778359773468178545674464}{9462790919736127661}\cdot t^5+\frac{103947145960380592834582465716000}{9462790919736127661}\cdot t^4-\frac{60913979792079425097574186512000}{9462790919736127661}\cdot t^3+\frac{18343437855919060890332066002560}{9462790919736127661}\cdot t^2-\frac{2327060033404462374818105053440}{9462790919736127661}\cdot t+\frac{84114286100757541224523825920}{9462790919736127661}$

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.