Inequalities for integrals of the modified Struve function of the first kind II

TL;DR

This paper derives simple, tight inequalities for integrals involving the modified Struve function of the first kind, which also lead to bounds for a related hypergeometric function, enhancing analytical tools in special functions.

Contribution

It introduces new tight inequalities for integrals of the modified Struve function, extending the understanding of their bounds and applications to hypergeometric functions.

Findings

Established tight inequalities for integrals of the modified Struve function.

Derived a double inequality involving the modified Struve function and hypergeometric functions.

Provided bounds that are tight in certain limits.

Abstract

Simple inequalities are established for integrals of the type $\int_0^x \mathrm{e}^{-\gamma t} t^{-\nu} \mathbf{L}_\nu(t)\,\mathrm{d}t$, where $x>0$, $0\leq\gamma<1$, $\nu>-\frac{3}{2}$ and $\mathbf{L}_{\nu}(x)$ is the modified Struve function of the first kind. In most cases, these inequalities are tight in certain limits. As a consequence we deduce a tight double inequality, involving the modified Struve function $\mathbf{L}_{\nu}(x)$, for a generalized hypergeometric function.