Contiguous Relations, Laplace's Methods and Continued Fractions for 3F2(1)

2017/09/01 by Akihito Ebisu, Ebisu, Akihito, Katsunori Iwasaki +1
Mathematics · #30B70 #30E10 (Secondary) #33C20 (Primary) #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1709.00159

openalex publication_date 2017/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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