A sequence involving an extended Struve function via a differential operator

Abstract

Various extensions of the Struve function have been presented and investigated. Here we aim to introduce an extended Struve function involving the $\mathtt{k}$-gamma function. Then, by using a known differential operator, we introduce a sequence of functions associated with the above introduced extended Struve function and investigate its properties such as generating relations and a finite summation formula. The results presented here, being very general, are also pointed out to yield a number of relatively simple identities.