Contiguous Relations, Laplace's Methods and Continued Fractions for 3F2(1)
Classical Analysis and ODEs
2017-09-04 v1
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.
Cite
@article{arxiv.1709.00159,
title = {Contiguous Relations, Laplace's Methods and Continued Fractions for 3F2(1)},
author = {Akihito Ebisu and Katsunori Iwasaki},
journal= {arXiv preprint arXiv:1709.00159},
year = {2017}
}
Comments
45 pages, 4 tables