A generalization of Clausen’s identity. (English) Zbl 1232.33003
Summary: 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 \(_{3}\)F\(_{2}\) 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.
MSC:
| 33C05 | Classical hypergeometric functions, \({}_2F_1\) |
| 33C65 | Appell, Horn and Lauricella functions |
| 32A10 | Holomorphic functions of several complex variables |
References:
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