Title: Contiguous Relations, Laplace's Methods and Continued Fractions for 3F2(1),
Abstract: Using contiguous relations we construct an infinite number of continued
fraction expansions for ratios of generalized hypergeometric series 3F2(1). We
establish exact error term estimates for their approximants and prove their
rapid convergences. To do so we develop a discrete version of Laplace's method
for hypergeometric series in addition to the use of ordinary (continuous)
Laplace's method for Euler's hypergeometric integrals.