Closed expressions for some infinite series of Bessel and Struve 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...

Some integrals involving generalized k-Struve functions

The close form of some integrals involving recently developed generalized k-Struve functions is obtained. The outcome of these integrations is expressed in terms of generalized Wright functions. Several special cases are deduced which lead to some known results.

Closed-form sums for some perturbation series involving hypergeometric functions

Infinite series of the type ∞ ∑ n=1 ( 2 )n n 1 n! 2F1(−n, b; γ; y) are investigated. Closed-form sums are obtained for α a positive integer α = 1, 2, 3, . . . . The limiting case of b → ∞, after y is replaced with x2/b, leads to ∞ ∑ n=1 ( 2 )n n 1 n! 1F1(−n, γ, x2). This type of series appears in the first-order perturbation correction for the wavefunction of the generalized spiked harmonic osc...

Some Distributions Involving Bessel Functions

Some Inequalities for Modified Bessel Functions

We denote by Iν and Kν the Bessel functions of the first and third kind, respectively. Motivated by the relevance of the function wν t t Iν−1 t /Iν t , t > 0, in many contexts of applied mathematics and, in particular, in some elasticity problems Simpson and Spector 1984 , we establish new inequalities for Iν t /Iν−1 t . The results are based on the recurrence relations for Iν and Iν−1 and the ...