Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8959555 | Journal of Mathematical Analysis and Applications | 2018 | 20 Pages |
Abstract
We obtain a simple two-sided inequality for the ratio Lν(x)/Lνâ1(x) in terms of the ratio Iν(x)/Iνâ1(x), where Lν(x) is the modified Struve function of the first kind and Iν(x) is the modified Bessel function of the first kind. This result allows one to use the extensive literature on bounds for Iν(x)/Iνâ1(x) to immediately deduce bounds for Lν(x)/Lνâ1(x). We note some consequences and obtain further bounds for Lν(x)/Lνâ1(x) by adapting techniques used to bound the ratio Iν(x)/Iνâ1(x). We apply these results to obtain new bounds for the condition numbers xLνâ²(x)/Lν(x), the ratio Lν(x)/Lν(y) and the modified Struve function Lν(x) itself. Amongst other results, we obtain two-sided inequalities for xLνâ²(x)/Lν(x) and Lν(x)/Lν(y) that are given in terms of xIνâ²(x)/Iν(x) and Iν(x)/Iν(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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Robert E. Gaunt,