An Inequality Involving Bessel Functions of Argument Nearly Equal to Their Order

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.

An Automatic Integration of Infinite Range Integrals Involving Bessel Functions

An efficient automatic quadrature procedure is developed for numerically computing the integrals 0 , where the function is smooth and nonoscillatory at infinity and is the Bessel functions of order ν =1,0 and 1/4. The procedure involves the use of an automatic integration scheme of modified FFT used for evaluating Fourier integrals and product type integration, and the modified W-transformation...

Redheffer Type Inequality for Bessel Functions

In this short note, by using mathematical induction and infinite product representations of the functions Jp : R → (−∞, 1] and Ip : R → [1,∞), defined by Jp(x) = 2Γ(p + 1)xJp(x) and Ip(x) = 2Γ(p + 1)xIp(x), an extension of Redheffer’s inequality for the function Jp and a Redheffer-type inequality for the function Ip are established. Here Jp and Ip, denotes the Bessel function and modified Besse...