On one sum of Hankel–Clifford integral transforms of Whittaker functions

In [11], the authors considered the realization $T$ of $SO(2,2)$-representation in a space of homogeneous functions on $2\times4$-matrices. In this sequel, we aim to compute matrix elements of the identical operator $T(e)$ and representation operator $T(g)$ for an appropriate $g$ with respect to the mixed basis related to two different bases in the $SO(2,2)$-carrier space and evaluate some improper integrals involving a product of Bessel-Clifford and Whittaker functions. The obtained result can be rewritten in terms of Hankel-Clifford integral transforms and their analogue. The first and the second Hankel-Clifford transforms introduced by Hayek and Pérez–Robayna, respectively, play an important role in the theory of fractional order differential operators (see, e.g., [6, 8]). The similar result have been derived recently by the authors for the regular Coulomb function in [12].