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The two most commonly used hypergeometric functions are the confluenthypergeometric function and the Gauss hypergeometric function. We review theavailable techniques for accurate, fast, and reliable computation of these twohypergeometric functions in different parameter and variable regimes. Themethods 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 numericalexperiments used to determine the best methods, in practice, for each parameterand variable regime considered. We provide 'roadmaps' with our recommendationfor which methods should be used in each situation.

Numerical Methods for the Computation of the Confluent and Gauss Hypergeometric Functions