Trigonometric expressions for Gaussian ${}_2F_1$ -series

Abstract

The classical Gaussian 2F1 -series containing two free variables fx; yg and two integer parameters fm; ngare investigated by the linearization method. Several closed formulae are derived in terms of trigonometric functions.Some of them are lifted up, via a trigonometric integral approach, to identities of nonterminating 3F2 -series.