Some expansions associated with Bessel functions

An Expansion for the Product of Two Bessel Functions.-1.1. An expansion for the product of two Bessel functions obtained by one of us(1) led to the discovery of a different expansion for the said product multiplied by the leading terms in the power series for the Bessel functions. Two proofs of this second expansion are given here

Inverse Problems of a Fractional Differential Equation with Bessel Operator

Inverse initial and inverse source problems of a time-fractional differential equation with Bessel operator are considered. Results on existence and uniqueness of solutions to these problems are presented. The solution method is based on series expansions using a set of Bessel functions of order zero. Convergence of the obtained series solutions is also discussedComment: 11 pages, No figure