Elliptic functions from hypergeometric integrals

2020/08/03 by P. L. Robinson, Robinson, P. L.
Mathematics · #33E05 #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2008.01240

openalex publication_date 2020/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

As a contribution to the Ramanujan theory of elliptic functions to alternative bases, Li-Chien Shen has shown how analogues of the Jacobian elliptic functions may be derived from incomplete hypergeometric integrals in signatures three and four. We determine precisely the signatures in which the Jacobian analogues or their squares are indeed elliptic.

Related

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• Elliptic functions from F((1)/(4), (3)/(4) ; (1)/(2) ; \bullet)
• Nonelliptic functions from F((1)/(6), (5)/(6) ; (1)/(2) ; \bullet)
• The elliptic function \rm dn₃ of Shen
• Elliptic functions from F((1)/(3), (2)/(3) ; (1)/(2) ; \bullet)