The Ramanujan Journal

, 26:133 | Cite as

A generalization of Clausen’s identity



The paper gives an extension of Clausen’s identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related third-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 as well. The related Chaundy’s identity is generalized without any restriction on the parameters of the Gauss hypergeometric function. The special case of dihedral Gauss hypergeometric functions is underscored.


Gauss hypergeometric function Bivariate hypergeometric series 

Mathematics Subject Classification (2000)

33C05 33C65 32A10 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.OASTKobe UniversityKobeJapan

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