Hypergeometric identities in elliptic signature six

2020/09/12 by P. L. Robinson, Robinson, P. L.
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2009.07069

Abstract

Within the Ramanujan theories of elliptic functions, Li-Chien Shen constructed natural elliptic functions in signature three and signature four. When applied in signature six, the same constructions produce non-elliptic functions that nevertheless engender the corresponding hypergeometric identities of Ramanujan.

Related

• Elliptic functions in signature four
• Elliptic functions from hypergeometric integrals
• The elliptic function \rm dn₃ of Shen
• The elliptic function \rm dn₂ of Shen
• A root elliptic function in signature four