New $q$-identities Via $q$-Derivative of Basic Hypergeometric Series with Respect to Parameters

In this paper, we use the effect of the $q$-differential and deformed $q$-exponential operators on basic hypergeometric series to find new $q$-identities from the $q$-Gauss sum, the $q$-Chu-Vandermonde’s sum, and Jackson’s transformation formula.