explorations on elementary mathematics and physics: some relations on bessel functions

Relations and identities on special functions are traditionally emerging from investigations on mathematical analysis. however, some special functions such as bessel appear in various physical problems, a way which some of their properties can be analyzed. there are plenty of identities on special functions which have been derived in such a way, especially some elementary problems in basic physics play interesting rule on this. uniformly charged disk of electrostatic is such a problem where appears unexpectedly in some cases. we study it more here and find some relations on bessel functions.