The aim of the present investigation is to create some summation theorems like Gauss, Bailey, and Kummer in the form of $k$- hypergeometric function. Further, we develop a new class of Kummer’s differential equation of $k$-parameter and Kummer’s transformations formulae in terms $k$- confluent hypergeometric function.
Keywords and Phrases
$k$-Gamma function, $k$-Beta function, $k$-hypergeometric functions, $k$-pochhammer symbols.
A.M.S. subject classiﬁcation
33E12, 44A10, 33B15.