Nonelliptic functions from F((1)/(6), (5)/(6) ; (1)/(2) ; \bullet)

2020/04/12 by P. L. Robinson, Robinson, P. L.
Mathematics · #33C05 #33E05 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2004.06529

openalex publication_date 2020/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

As contributions to the Ramanujan theory of elliptic functions to alternative bases, Li-Chien Shen has developed families of elliptic functions from the hypergeometric functions F(\tfrac13, \tfrac23; \tfrac12 ; \bullet) and F(\tfrac14, \tfrac34; \tfrac12 ; \bullet). We apply his methods to the hypergeometric function F(\tfrac16, \tfrac56; \tfrac12 ; \bullet).

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