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

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 $x>0$, $0\le \gamma <1$, $\nu >-\frac{3}{2}$ 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.

9 pages. arXiv admin note: text overlap with arXiv:1806.00524, arXiv:1802.02221