Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions

Abstract

In this paper, we investigate the relationships among hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions through some families of `hypergeometric' algebraic varieties that are higher dimensional analogues of Legendre curves.

25 pages

References in corpus (5)

• Ramanujan-type supercongruences
• Generalized Legendre curves and Quaternionic Multiplication
• Atkin and Swinnerton-Dyer congruences and noncongruence modular forms
• Some supercongruences occurring in truncated hypergeometric series
• A finite field hypergeometric function associated to eigenvalues of a Siegel eigenform

Cited by in corpus (3)

• Generalized Legendre curves and Quaternionic Multiplication
• $p$-adic analogues of hypergeometric identities
• A Cubic Transformation Formula for Appell-Lauricella Hypergeometric Functions over Finite Fields