Abstract
Many of the Physical, Astrophysical, Statistical, and Mathematical problems can be solved by using the allied special functions. Specifically, various multiple hypergeometric series and reduction formulae can be applied to solve such problems. The aim of the present chapter is to derive certain classes of the reduction formulae for the Srivastava–Daoust type doublehypergeometric series. To prove these reductions, we use one of the extension results on the Bailey transform developed and studied by Joshi and Vyas in 2005.We also obtain some well–known formulae, e.g. the Kampé de Fériet reduction formula, the Euler transformation formula and Whipple’s quadratic transformation formula, on particularization of some reduction formulae. 2020 Mathematics Subject Classification. 33C05; 33C15; 33C65
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