Computation of hyperngeometric functions for gravitationally radiating binary stars

Abstract

The exact solution for any eccentricity of the Peters-Mathews model of binary stars emitting gravitational waves leads to hypergeometric functions of Appell and Gauss type. Efficient (fast and accurate) numerical computations of such functions can be obtained by using the Pade approximation. Pade rational approximants, for equal numbers of coefficients, are more accurate than Taylor series representation. Unfortunately, the algorithm computing Pade coefficients numerically from Taylor series is known to be unstable. This numerical instability lowers the accuracy of the Pade approximant. In this paper, double precision accuracy Pade approximant coefficients are computed symbolically. Advantages of the symbolic computation with respect to the numerical treatment are shown, providing accurate representations of the Appell and Gauss hypergeometric functions. The symbolic approach can be extended to higher post-Newtonian models.