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Numerical methods for the computation of the confluent and Gauss hypergeometric functions

Pearson, John W, Olver, Sheehan, Porter, Mason A (2017) Numerical methods for the computation of the confluent and Gauss hypergeometric functions. Numerical Algorithms, 74 (3). pp. 821-866. ISSN 1017-1398. (doi:10.1007/s11075-016-0173-0) (KAR id:48161)


The two most commonly used hypergeometric functions are the confluent hypergeometric function and the Gauss hypergeometric function. We review the available techniques for accurate, fast, and reliable computation of these two hypergeometric functions in different parameter and variable regimes. The methods that we investigate include Taylor and asymptotic series computations, Gauss-Jacobi quadrature, numerical solution of differential equations, recurrence relations, and others. We discuss the results of numerical experiments used to determine the best methods, in practice, for each parameter and variable regime considered. We provide 'roadmaps' with our recommendation for which methods should be used in each situation.

Item Type: Article
DOI/Identification number: 10.1007/s11075-016-0173-0
Uncontrolled keywords: Computation of special functions; Confluent hypergeometric function; Gauss hypergeometric function
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: John Pearson
Date Deposited: 30 Apr 2015 17:10 UTC
Last Modified: 08 Dec 2022 20:34 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

Pearson, John W.

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