New g-analogue of modified Bessel function and the quantum algebra Eq{2).

In this paper, a new q-analogue of modified Bessel function and its corresponding gen-erating function are given. Also, we used the generating function method to deduce its q--difference equation which gives us the differential equation of the ordinary modified Bessel function when q → 1 and we deduced its recurrence relation. Finally, we established the relation between the two-dimensional quantum algebra Eq(2) and the new q--analogue of modified Bessel function using the realization of the standard Euclidean algebra in one real variable and q--exponentials. [ABSTRACT FROM AUTHOR]