Tables for the evaluation of ∫₀^{∞}𝑥^{𝛽}𝑒^{-𝑥}𝑓(𝑥)𝑑𝑥 by Gauss-Laguerre quadrature

Abstract

Tables of abscissae and weight coefficients to fifteen places are presented for the Gauss-Laguerre quadrature formula ∫ 0 ∞ x β e − x f ( x ) d x ∼ ∑ k = 1 n H k f ( a k ) \int _0^\infty {{x^\beta }{e^{ - x}}f(x)dx \sim \sum \limits _{k = 1}^n {{H_k}f({a_k})} } for β = − 1 4 , − 1 2 , and − 3 4 \beta = - \tfrac {1}{4}, - \tfrac {1}{2},{\text {and}} - \tfrac {3}{4} and n = 1(1)15.