Rule: Q[1, 3, 8]

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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^4+\frac{49}{4}\cdot t^3-\frac{153}{4}\cdot t^2+\frac{57}{2}\cdot t-\frac{3}{2}$
• $P_3$:
  $-t^{12}+\frac{2070953589220306847}{12642861578110780}\cdot t^{11}-\frac{645525472215747960019}{63214307890553900}\cdot t^{10}+\frac{10374715474075977921763}{31607153945276950}\cdot t^9-\frac{38483830014145465893501}{6321430789055390}\cdot t^8+\frac{1078888160478032669504712}{15803576972638475}\cdot t^7-\frac{7404981491515842752966952}{15803576972638475}\cdot t^6+\frac{30707272268138136735760752}{15803576972638475}\cdot t^5-\frac{14813801719515827550292176}{3160715394527695}\cdot t^4+\frac{3871347661564847026518816}{632143078905539}\cdot t^3-\frac{12056710512578600263939488}{3160715394527695}\cdot t^2+\frac{2778231243783503110252608}{3160715394527695}\cdot t-\frac{122456901777781747071168}{3160715394527695}$

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.