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

My paper on computation of confluent and Gauss hypergeometric functions, from a project that started in Spring 2009, finally is not only out in a journal but now even has coordinates (volume, page numbers, etc.) Here are the details.

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

Authors: John W. Pearson, Sheehan Olver, and Mason A. Porter

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. 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 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.

Our Matlab code is available from this website.