New series expansions of the 3F2 function

Esta es la versión no revisada del artículo: José L. López, Pedro Pagola, Ester Pérez Sinusía, New series expansions of the 3F2 function. J. Math. Anal. Appl, 421 (2015) 982-995. Pages 982-995, ISSN 0022-247X. Se puede consultar la versión publicada en https://doi.org/10.1016/j.jmaa.2014.07.065.We can use the power series definition of 3F2(a1, a2, a3; b1, b2; z) to compute this function for z in the unit disk only. In this paper we obtain new expansions of this function that are convergent in larger domains. Some of these expansions involve the polynomial 3F2(a1,−n, a3; b1, b2; z) evaluated at certain points z. Other expansions involve the Gauss hypergeometric function 2F1. The domain of convergence is sometimes a disk, other times a half-plane, other times the region |z|2 < 4|1 − z|. The accuracy of the approximation given by these expansions is illustrated with numerical experiments.The authors acknowledge Dirección General de Ciencia y Tecnología (grant No. MTM2010-21037) for financial support