A generalization of Clausen's identity

Abstract

The paper aims to generalize Clausen's identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related 3rd order linear differential equation are found in terms of certain bivariate series that can reduce to 3F2 series similar to those in Clausen's identity. The general contiguous variation of Clausen's identity is found. The related Chaundy's identity is generalized without any restriction on the parameters of Gauss hypergeometric function. The special case of dihedral Gauss hypergeometric functions is underscored.

References in corpus (4)

• Identities between Appell's and hypergeometric functions
• The time-dependent Schroedinger equation, Riccati equation and Airy functions
• Transformations and invariants for dihedral Gauss hypergeometric functions
• On singular univariate specializations of bivariate hypergeometric functions

Cited by in corpus (6)

• Dihedral Gauss hypergeometric functions
• A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds
• Transformations and invariants for dihedral Gauss hypergeometric functions
• On singular univariate specializations of bivariate hypergeometric functions
• On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums
• P-finite Recurrences From Generating Functions with Roots of Polynomials