Uniform bounds for expressions involving modified Bessel functions

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.

Inequalities for Integrals of Modified Bessel Functions and Expressions Involving Them

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We apply these inequalities to obtain uniform bounds for several expressions involving integrals of modified Bessel functions. Such expressions occur in Stein’...

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...

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.