Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions

DOI10.1016/S0377-0427(01)00383-1zbMath0998.65032WikidataQ126844185 ScholiaQ126844185MaRDI QIDQ5957975

Walter Gautschi

Publication date: 15 November 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

error boundsGauss quadraturehypergeometric functionconfluent hypergeometric functionsderivative-free contour integral representation

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items

New series expansions for the confluent hypergeometric function \(M(a,b,z)\) ⋮ Implicit-explicit time integration of nonlinear fractional differential equations ⋮ A characterization of the distribution of a weighted sum of gamma variables through multiple hypergeometric functions ⋮ Acceleration of generalized hypergeometric functions through precise remainder asymptotics ⋮ Numerical methods for the computation of the confluent and Gauss hypergeometric functions ⋮ Numerical model for macroscopic quantum superpositions based on phase-covariant quantum cloning ⋮ Identifying the computational problem in applied statistics

Uses Software

• ORTHPOL

Cites Work

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• On the numerical solution of Cauchy type singular integral equations and the determination of stress intensity factors in case of complex singularities
• Error Bounds for Gaussian Quadrature of Analytic Functions
• Gaussian Integration for Complex Weight Functions
• Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules
• Computational Aspects of Three-Term Recurrence Relations
• Uniform Asymptotic Expansions of the Jacobi Polynomials and an Associated Function
• A Unified Approach to Quadrature Rules with Asymptotic Estimates of Their Remainders