Bounds for an integral involving the modified Lommel function of the first kind

DOI10.1007/S00025-022-01679-4arXiv2103.16666WikidataQ114231946 ScholiaQ114231946MaRDI QIDQ6364167

Robert E. Gaunt

Publication date: 30 March 2021

Abstract: Simple upper and lower bounds are established for the integral $$, where $x>0$, $$, $mu+u>-2$, $mu-ugeq-3$, and $t_{mu,u}(x)$ is the modified Lommel function of the first kind. Our bounds complement and improve on existing bounds for this integral, by either being sharper or increasing the range of validity. Our bounds also generalise recent bounds for an integral involving the modified Struve function of the first kind, and in some cases more a direct approach lead to sharper bounds when our general bounds are specialised to the modified Struve case.

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Generalized hypergeometric series, ({}_pF_q) (33C20)

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