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.
Highlights
Various extensions of the Struve function have been presented and investigated
By using operational techniques, we introduce a sequence of operators (2.5) involving the extended Struve function (1.8) and investigate its generating relations and finite summation formulas
By modifying the sequence in (2.4), we introduce a sequence of operators involving the extended Struve function (1.8)
Summary
Abstract: Various extensions of the Struve function have been presented and investigated. We aim to introduce an extended Struve function involving the k-gamma function. 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. We begin by recalling the Struve function and its generalizations. Bhowmick [7] extended the Struve function in (1.1) as follows: Hlλ(x). We recall the following extended Struve function (see [25]; see [24]). By using operational techniques, we introduce a sequence of operators (2.5) involving the extended Struve function (1.8) and investigate its generating relations and finite summation formulas.
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