Extensions of the classical theorems for very well-poised hypergeometric functions
arXiv:1410.3241 · doi:10.1007/s13398-017-0485-5
Abstract
The classical summation and transformation theorems for very well-poised hypergeometric functions, namely, summation, Dougall's summation, Whipple's to transformation and Bailey's to transformation are extended. These extensions are derived by applying the well-known Bailey's transform method along with the classical very well-poised summation and transformation theorems for very well-poised hypergeometric functions and the Rakha and Rathie's extension of the Saalschütz's theorem. To show importance and applications of the discovered extensions, a number of special cases are pointed out, which leads not only to the extensions of other classical theorems for very well-poised and well-poised hypergeometric functions but also generate new hypergeometric summations and transformations.
14 pages. "This is a pre-print of (a part of) an article published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas (RACSAM). The final authenticated version is available online at: https://doi.org/10.1007/s13398-017-0485-5 "