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In this paper, we obtain inequalities for some integrals involving the modified Lommel function of the first kind $t_{\mu,\nu}(x)$. In most cases, these inequalities are tight in certain limits. We also deduce a tight double inequality, involving the modified Lommel function $t_{\mu,\nu}(x)$, for a generalized hypergeometric function. The inequalities obtained in this paper generalise recent bounds for integrals involving the modified Struve function of the first kind.

Inequalities for Some Integrals Involving Modified Lommel Functions of the First Kind