Unification of Bessel Functions of Different Orders

We investigate the internal space of Bessel functions which is associated to thegroup Z of positive and negative integers defining their orders. As a result wepropose and prove a new unifying formula (to be added to the huge literatureon Bessel functions) generating Bessel functions of real orders out of integerorder ones. The unifying formula is expected to be of great use in appliedmathematics. Some applications of the formula are given for illustration