SUMMATIONS AND TRANSFORMATIONS FOR VERY WELL-POISED HYPERGEOMETRIC FUNCTIONS 2q+5F2q+4(1) AND 2q+7F2q+6(1) WITH ARBITRARY INTEGRAL PARAMETER DIFFERENCES

摘要

The present paper aims to derive summation and transformation formulae for the generalized very well-poised hypergeometric functions 2q+5F2q+4(1) and 2q+7F2q+6(1) having arbitrary integral parameter differences. These results are derived with the help of Bailey's transform and the extension of Saalschu center dot tz summation theorem for the series r+3Fr+2(1), where r pairs of parameters differ by positive integers. The particularizations of these generalized identities give classical summation theorems due to Dougall, transformation formula due to Whipple and, other related results. Furthermore, the application of 2q+5F2q+4(1) summation to the limiting case, when q -* 1, of one of the Andrews' q-identities gives a Srivastava-Daoust type multiple hypergeometric series.