Some new thoughts on Gauss–Laguerre quadrature

Abstract

Gauss–Laguerre quadrature is notoriously poor for integrating non-exponentially decreasing infinite-range integrals. A method is proposed based on the non-standard basis set 1/x ⁱ and this is implemented for the weight functions 1.0, log x and sin x. A series of tests demonstrate the effectiveness of the approach, and an algorithm is presented to achieve convergence to a specified accuracy.

Keywords:

• Infinite range quadrature
• Gauss–Laguerre
• Non-exponentially decreasing integrands