Bounds for modified Bessel functions

Laforgia, Andrea

doi:10.1016/0377-0427(91)90087-z

Cited by 42 publications

(32 citation statements)

References 7 publications

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“…if and only if r 1 ≤ min (|v| , 1/2) and r 2 ≥ max (|v| , 1/2). Obviously, our inequalities (5.11) are superior to those earlier results appeared in [46], [47], [48], [50], [49].…”

Section: Corollarycontrasting

confidence: 82%

Monotonicity rules for the ratio of two Laplace transforms with applications

Yang¹,

Tian²

2019

Journal of Mathematical Analysis and Applications

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Let f and g be both continuous functions on (0, ∞) with g (t) > 0 for t ∈ (0, ∞) and let F (x) = L (f ), G (x) = L (g) be respectively the Laplace transforms of f and g converging for x > 0. We prove that if there is a t * ∈ (0, ∞) such that f /g is strictly increasing on (0, t * ) and strictly decreasing on (t * , ∞), then the ratio F/G is decreasing on (0, ∞) if and only if ∞ 0 e −x cosh t cosh (vt) dt, 2010 Mathematics Subject Classification. Primary 44A10, 26A48; Secondary 33B15, 33C10. Key words and phrases. Laplace transform, monotonicity rule, psi function, modified Bessel functions of the second kind.This paper is in final form and no version of it will be submitted for publication elsewhere.

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“…if and only if r 1 ≤ min (|v| , 1/2) and r 2 ≥ max (|v| , 1/2). Obviously, our inequalities (5.11) are superior to those earlier results appeared in [46], [47], [48], [50], [49].…”

Section: Corollarycontrasting

confidence: 82%

Monotonicity rules for the ratio of two Laplace transforms with applications

Yang¹,

Tian²

2019

Journal of Mathematical Analysis and Applications

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“…Furthermore, there are provided in [13] the following bounds for ratio I µ (y)/I µ (x) of modified Bessel functions of the first kind…”

Section: Notationmentioning

confidence: 99%

Exit times densities of the Bessel process

Serafin

2017

Proc. Amer. Math. Soc.

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We examine the density functions of the first exit times of the Bessel process from the intervals [0, 1) and (0, 1). First, we express them by means of the transition density function of the killed process. Using that relationship we provide precise estimates and asymptotics of the exit time densities. In particular, the results hold for the first exit time of the n-dimensional Brownian motion from a ball.2010 Mathematics Subject Classification. 60J60, 60J65.

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“…There is now an extensive literature on lower and upper bounds for these ratios; see [1,5,14,15,17,18,19,26,27,31,32,36,38,39,40,43]. There is also a considerable literature on lower and upper bounds for the ratios I ν (x)/I ν (y) and K ν (x)/K ν (y); see [1,2,4,10,11,17,20,21,24,25,35,37,42], which has been used, for example, to obtain tight bounds for the generalized Marcum Q-function, which arises in radar signal processing [2,10].…”

Section: Introductionmentioning

confidence: 99%