Rule: Q[6, 11]

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.

• $P_1$:
  $\frac{1}{720}\cdot t^6-\frac{1}{20}\cdot t^5+\frac{5}{8}\cdot t^4-\frac{10}{3}\cdot t^3+\frac{15}{2}\cdot t^2-6\cdot t+1$
• $P_2$:
  $\frac{1}{720}\cdot t^{17}-\frac{260322918421133747}{844950285602589600}\cdot t^{16}+\frac{353975289260728444493}{11829303998436254400}\cdot t^{15}-\frac{265330933228311436835}{157724053312483392}\cdot t^{14}+\frac{4809920475353750573485}{78862026656241696}\cdot t^{13}-\frac{118652649960935508711155}{78862026656241696}\cdot t^{12}+\frac{170699994176437952583631}{6571835554686808}\cdot t^{11}-\frac{2090286059813803789411111}{6571835554686808}\cdot t^{10}+\frac{9106779346366623864039955}{3285917777343404}\cdot t^9-\frac{56165460606775250848984185}{3285917777343404}\cdot t^8+\frac{60468125542062185548791630}{821479444335851}\cdot t^7-\frac{25383698538024516677687898}{117354206333693}\cdot t^6+\frac{49132387645944610136236668}{117354206333693}\cdot t^5-\frac{59398105123945501050089700}{117354206333693}\cdot t^4+\frac{41274177373030983131480400}{117354206333693}\cdot t^3-\frac{14284310016781250519634000}{117354206333693}\cdot t^2+\frac{1820432575969290394388640}{117354206333693}\cdot t-\frac{30709685533112203004640}{117354206333693}$

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.