Bounds for functions involving ratios of modified Bessel functions

Some Integrals Involving Bessel Functions Some Integrals Involving Bessel Functions

A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of pr...

Uniform Bounds for Bessel Functions

For ν > −1/2 and x real we shall establish explicit bounds for the Bessel function Jν(x) which are uniform in x and ν. This work and the recent result of L. J. Landau [7] provide relatively sharp inequalities for all real x.

Computation of Modified Bessel Functions and Their Ratios

An efficient algorithm for calculating ratios rv(x) = I,+,(x)/IAx), v â 0, x ä 0, is presented. This algorithm in conjunction with the recursion relation for rAx) gives an alternative to other recursive methods for I Ax) when approximations for low-order Bessel functions are available. Sharp bounds on r,(x) and IAx) are also established in addition to some monotonicity properties of ry(x) and r...

Some Distributions Involving Bessel Functions

Inequalities Involving Generalized Bessel Functions

Let up denote the normalized, generalized Bessel function of order p which depends on two parameters b and c and let λp(x) = up(x), x ≥ 0. It is proven that under some conditions imposed on p, b, and c the Askey inequality holds true for the function λp , i.e., that λp(x) +λp(y) ≤ 1 +λp(z), where x, y ≥ 0 and z = x + y. The lower and upper bounds for the function λp are also established.