Certain relations between Bessel and Whittaker functions related to some diagonal and block-diagonal 3 ˣ 3-matrices

The authors derive the matrix elements of the linear operators which appear under the representation of the group SO(2, 1) and correspond to some diagonal or block-diagonal matrices belonging to the above group. Then, by applying these matrix elements, that is, from a group theoretical point of view, the authors show how certain interesting integral and series represen- tations of the Whittaker function of the second kind and some formulas for the (basic and modified) Bessel functi ns can be obtained. A special case of one of the results presented here is indicated to be also a special one of a known formula.