  In the article [11] of L. Kunyansky a symmetric integral identity for Bessel
functions of the first and second kind was proved in order to obtain an
explicit inversion formula for the spherical mean transform where our data is
given on the unit sphere in $\Bbb R^{n}$. The aim of this paper is to prove an
analogous symmetric integral identity in case where our data for the spherical
mean transform is given on an ellipse $E$ in $\Bbb R^{2}$. For this, we will
use the recent results obtained by H.S. Cohl and H.Volkmer in [7] for the
expansions into eigenfunctions of Bessel functions of the first and second kind
in elliptical coordinates.
