Representation of Lie algebra T3 and 2-variable 2-parameter Bessel functions

In this paper, we deal with the problem of framing 2-variable 2-parameter Bessel functions (2V2PBF) into the context of the representation Q(w,m0) of the 3-dimensional Lie algebra T3. Further, we derive generating relations and identities involving 2V2PBF. Furthermore, we deduce some new and known relations involving various other forms of generalized Bessel functions (GBF) and Bessel functions (BF) as applications of these results.