Approximations for the renewal function

This paper describes an accurate, computable approximation for evaluating the renewal function (RF). The method uses Pade approximants to compute the RF near the origin and switches to the asymptotic values farther from the origin. There is a polynomial switch-over function in terms of the coefficient of variation of the distribution, enabling one to determine a priori if the asymptotic value can be used instead of computing the Pade approximant. The results are tested with the truncated Gaussian distribution. The method yields a set of approximants to the RF that are re-usable, and can be used to compute the derivative and the integral of the RF. Results for the RF are within 1% of the optimal solution for most coefficients of variation