Unification of Bessel functions of different orders

Abstract

We investigate the internal space of Bessel functions which is associated to the group Z of positive and negative integers defining their orders. As a result we propose and prove a new unifying formula (to be added to the huge literature on Bessel functions) generating Bessel functions of real orders out of integer order one's. The unifying formula is expected to be of great use in applied mathematics. Some applications of the formula are given for illustration.