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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:468

Article

Gaunt, Robert E.¹ 

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

关键词: Modified Struve function of the first kind;    Bounds;    Ratios of modified Struve functions;    Condition numbers;    Modified Bessel function of the first kind;   

DOI  :  10.1016/j.jmaa.2018.08.043

来源: Elsevier

【 摘 要 】

We obtain a simple two-sided inequality for the ratio L-nu(x)/L nu-1(x) in terms of the ratio I-nu(x)/I nu-1(x), where L-nu(x) is the modified Struve function of the first kind and I-nu(x) is the modified Bessel function of the first kind. This result allows one to use the extensive literature on bounds for I-nu(x)/I nu-1(x) to immediately deduce bounds for L-nu(x)/L nu-1(x). We note some consequences and obtain further bounds for L-nu(x)/L nu-1(x) by adapting techniques used to bound the ratio I-nu(x)/I nu-1(x). We apply these results to obtain new bounds for the condition numbers xL(nu)'(x)/L-nu(x), the ratio L-nu(x)/L-nu(y) and the modified Struve function L-nu(x) itself. Amongst other results, we obtain two-sided inequalities for xL(nu)'(x)/L-nu(x) and L-nu(x)/L-nu(y) that are given in terms of xI(nu)'(x)/I-nu(x) and I-nu(x)/I-nu(y), 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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