Certain inequalities involving the k-Struve function

TL;DR

This paper introduces the k-Struve function, explores its properties including inequalities related to Turán type inequalities, and provides differential equations, recurrence relations, and integral representations.

Contribution

It is the first to define the k-Struve function and analyze its fundamental properties and inequalities, expanding the understanding of special functions.

Findings

Derived inequalities related to the k-Struve function

Established differential equations and recurrence relations

Presented integral representations of the k-Struve function

Abstract

We aim to introduce a $\mathtt{k}$-Struve function and investigate its various properties, including mainly certain inequalities associated this function. One of the inequalities given here is pointed out to be related to the so-called classical Tur\'an type inequality. We also present a differential equation, several recurrence relations, and integral representations for this $\mathtt{k}$-Struve function.