Dual and triple Fourier-Bessel series equations

Abstract

A method for solving dual and triple Fourier-Bessel series equations is proposed. It is based on a novel operator transforming Bessel functions into the sine function and on an inversion formula analogous to one for Bessel series. As a result, the dual and triple equations are transformed into the Fredholm integral equations of the second kind or into the singular integral equations of a well-known type. The suggested approach differs from the existing and provides new possibilities for applications. This is demonstrated by the torsional problem for an annular punch in contact with an inhomogeneous elastic cylinder. The asymptotic solution is derived as a distance between the punch edge and the lateral cylinder surface is short provided that the punch hole is small. A number of novel results for series containing Bessel functions is obtained as well.