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

John Pearson, Sheehan Olver, Mason A. Porter

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)821-866
Number of pages42
JournalNumerical Algorithms
Volume74
Issue number3
Early online date27 Aug 2016
DOIs
Publication statusPublished - Mar 2017

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