Bounds for modified Struve functions of the first kind and their ratios

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    Abstract

    We obtain a simple two-sided inequality for the ratio in terms of the ratio , where is the modified Struve function of the first kind and is the modified Bessel function of the first kind. This result allows one to use the extensive literature on bounds for to immediately deduce bounds for . We note some consequences and obtain further bounds for by adapting techniques used to bound the ratio . We apply these results to obtain new bounds for the condition numbers , the ratio and the modified Struve function itself. Amongst other results, we obtain two-sided inequalities for and that are given in terms of and , respectively, which again allows one to exploit the substantial literature on bounds for these quantities. The results obtained in this paper complement and improve existing bounds in the literature.
    Original languageEnglish
    Pages (from-to)547-566
    JournalJournal of Mathematical Analysis and Applications
    Volume468
    Issue number1
    Early online date27 Aug 2018
    DOIs
    Publication statusPublished - 1 Dec 2018

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