Abscissae and weights for the Gauss-Laguerre quadrature formula

✍ Scribed by Tadashi Takemasa

• Publisher: Elsevier Science
• Year: 1988
• Tongue: English
• Weight: 650 KB
• Volume: 52
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(88)90178-6

✦ Synopsis

A program is described which calculates the abscissae and weights for the Gauss-Laguerre quadrature formula for integrals of the form fẽ~x'f(x)dx very rapidly and with high accuracy even in the case of many abscissae. The abscissae are given by the zeros of the Laguerre polynomials, which are found by the Newton-Raphson method with suitable initial approximations. The program is useful for the problem in the case of an integrand f( x) oscillating rapidly.