An inversion formula for the distributional generalized Laplace transformation (Q1916713)

A generalization of the classical Laplace transform \[ L[f(t);s]= \int^\infty_0 e^{-st}f(t)dt, \qquad \text{Re}(s)>0, \] was given by \textit{H. M. Srivastava} [Mathematica, Cluj 10(33), 385-390 (1968; Zbl 0176.10202)] in the form \[ S^{(\rho,\sigma)}_{q,k,m} [f(t),s]=\int^\infty_0 (st)^{\sigma-1/2} e^{-qst/2} W_{k,m}(\rho st) f(t)dt, \tag \(*\) \] where \(W_{k,m}(z)\) denotes the Whittaker function of second kind. The authors in the present paper extend to Schwartz's distribution an inversion formula for the generalized Laplace transform \((*)\).