Results 11 to 20 of about 496,864 (207)
Some inequalities of Bessel and modified Bessel functions [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1991 AbstractTwo-sided inequalties for the ratio of modified Bessel functions of first kind are given, which provide sharper upper and lower bounds than had been known earlier. Wronskian type inequalities for Bessel functions are proved, and in the sequel alternative proofs of Turan-type inequalities for Bessel and modified Bessel functions are also ...
C. Joshi, S. K. Bissu
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Bounds for modified Bessel functions
Rendiconti del Circolo Matematico di Palermo, 1991 Aus Monotonieeigenschaften von \(I_{v+1}/I_ v\) und \(K_{v+1}/K_ v\) werden Schranken für \(I_ v\) und \(K_ v\) gewonnen und diskutiert.
A. Laforgia
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Computation of modified Bessel functions and their ratios [PDF]
Mathematics of Computation, 1974 An efficient algorithm for calculating ratios r v ( x ) = I v + 1 ( x ) / I v
By D. E. Amos
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Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions [PDF]
, 2014 In the paper, the author establishes inequalities, monotonicity, convexity, and unimodality for functions concerning the modified Bessel functions of the first kind and compute the completely monotonic degrees of differences between the exponential and ...
Qi, Feng
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A new type of sharp bounds for ratios of modified Bessel functions [PDF]
Journal of Mathematical Analysis and Applications, 2016 The bounds for the ratios of first and second kind modified Bessel functions of consecutive orders are important quantities appearing in a large number of scientific applications.
D. Ruiz-Antolín, J. Segura
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TURÁN TYPE INEQUALITIES FOR MODIFIED BESSEL FUNCTIONS [PDF]
Bulletin of the Australian Mathematical Society, 2010 AbstractIn this paper our aim is to deduce some sharp Turán type inequalities for modified Bessel functions of the first and second kinds. Our proofs are based on explicit formulas for the Turánians of the modified Bessel functions of the first and second kinds and on a formula which is related to the infinite divisibility of the Studentt-distribution.
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Inequalities involving Bessel and modified Bessel functions
Journal of Mathematical Analysis and Applications, 1990 The authors define a self-adjoint and compact operator whose eigenvalues are given by \(\pm 2/j_{\nu k}\), where \(j_{\nu k}\) is the kth positive zero of the Bessel function \(J_{\nu}(x)\) of the first kind. Using operator techniques the authors derive some lower and upper bounds for \(J_{\nu +1}(x)/J_{\nu}(x)\) and \(I_{\nu +1}(x)/I_{\nu}(x)\), where
E. K. Ifantis, P. Siafarikas
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Simple bounds with best possible accuracy for ratios of modified Bessel functions [PDF]
Journal of Mathematical Analysis and Applications, 2022 The best bounds of the form $B(\alpha,\beta,\gamma,x)=(\alpha+\sqrt{\beta^2+\gamma^2 x^2})/x$ for ratios of modified Bessel functions are characterized: if $\alpha$, $\beta$ and $\gamma$ are chosen in such a way that $B(\alpha,\beta,\gamma,x)$ is a sharp
J. Segura
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Jordan type inequalities involving the Bessel and modified Bessel functions
Computers & Mathematics with Applications, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ling Zhu
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Two general series identities involving modified Bessel functions and a class of arithmetical functions [PDF]
Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2022 We consider two sequences $a(n)$ and $b(n)$ , $1\leq ...
B. Berndt +3 more
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