Rule: Q[1, 4, 10]

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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^5+\frac{319}{15}\cdot t^4-\frac{2104}{15}\cdot t^3+\frac{1656}{5}\cdot t^2-\frac{1208}{5}\cdot t+\frac{152}{5}$
• $P_3$:
  $-t^{15}+\frac{5830422343941554964122137818045331}{35557989102486713135257466622735}\cdot t^{14}-\frac{1225428716499805027451255271654724438}{106673967307460139405772399868205}\cdot t^{13}+\frac{48307484340458023763182130568777743146}{106673967307460139405772399868205}\cdot t^{12}-\frac{18861518568005864845267159689247846456}{1693237576308891101678926982035}\cdot t^{11}+\frac{6376832840492207075190955821241852497944}{35557989102486713135257466622735}\cdot t^{10}-\frac{1960333344231738358743298674303636509968}{1015942545785334661007356189221}\cdot t^9+\frac{674069544431990743579521666273433561968}{48378216465968317190826485201}\cdot t^8-\frac{158652129719758013932115763933228216952704}{2370532606832447542350497774849}\cdot t^7+\frac{70876434058783298356706980017076009328256}{338647515261778220335785396407}\cdot t^6-\frac{139137180268099709687380467457183335961344}{338647515261778220335785396407}\cdot t^5+\frac{23137567759360338740269773815372774388480}{48378216465968317190826485201}\cdot t^4-\frac{102367083012143008160211307502154834447360}{338647515261778220335785396407}\cdot t^3+\frac{4388933284517437387267468526109883560960}{48378216465968317190826485201}\cdot t^2-\frac{519840090374987813749658822497710458880}{48378216465968317190826485201}\cdot t+\frac{123641184301787931019802193256384112640}{338647515261778220335785396407}$

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.