Numerical Evaluation of the Gauss Hypergeometric Function with the hypergeo Package

This paper introduces the hypergeo package of R routines for numerical calculation of hypergeometric functions. The package is focussed on efficient and accurate evaluation of the Gauss hypergeometric function over the whole of the complex plane within the constraints of fixed-precision arithmetic. The hypergeometric series is convergent only within the unit circle, so analytic continuation must be used to define the function outside the unit circle. This short document outlines the numerical and conceptual methods used in the package; and justifies the package philosophy, which is to maintain transparent and verifiable links between the software and Abramowitz and Stegun (1965). Most of the package functionality is accessed via the single function hypergeo(), which dispatches to one of several methods depending on the value of its arguments. The package is demonstrated in the context of game theory.