  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.
