Trigonometric expressions for Gaussian $_2F_1$-series

Authors : Wenchang Chu

Pages : 1823-1836

View : 12 | Download : 6

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :The classical Gaussian $_2F_1$-series containing two free variables $\{x,y\}$ and two integer parameters $\{m,n\}$ are 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 $_3F_2$-series.
Keywords : Classical hypergeometric series, Pfaff-Saalsch summation theorem, linearization method, Gould-Hsu inversions, trigonometric integral approach