Elliptic functions from F((1)/(3), (2)/(3) ; (1)/(2) ; \bullet)

2019/07/21 by P. L. Robinson, Robinson, P. L.
Mathematics · #33C05 #33E05 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1907.09938

openalex publication_date 2019/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Li-Chien Shen developed a family of elliptic functions from the hypergeometric function ₂F₁((1)/(3), (2)/(3) ; (1)/(2) ; \bullet). We comment on this development, offering some new proofs.

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• Nonelliptic functions from F((1)/(6), (5)/(6) ; (1)/(2) ; \bullet)
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• Elliptic functions from hypergeometric integrals
• Elliptic hypergeometric functions