Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1810-27
Keywords
Classical hypergeometric series, Pfaff-Saalsch summation theorem, linearization method, Gould-Hsu inversions, trigonometric integral approach
First Page
1823
Last Page
1836
Recommended Citation
CHU, W (2019). Trigonometric expressions for Gaussian $_2F_1$-series. Turkish Journal of Mathematics 43 (4): 1823-1836. https://doi.org/10.3906/mat-1810-27
