Whittaker transform

The integral transform

$$F(x)=\int\limits_0^\infty(2xt)^{-1/4}W_{\lambda,\mu}(2xt)f(t)\,dt,$$

where $W_{\lambda,\mu}(z)$ is the Whittaker function (cf. Whittaker functions). For $\lambda=1/4$ and $\mu=\pm1/4$ the Whittaker transform goes over into the Laplace transform.

References

[1]	C.S. Meijer, "Eine neue Erweiterung der Laplace-Transformation" Proc. Koninkl. Ned. Akad. Wet. , 44 (1941) pp. 727–737
[a1]	G. Doetsch, "Handbuch der Laplace-Transformation" , III , Birkhäuser (1973)
[a2]	E.T. Whittaker, G.N. Watson, "A course of modern analysis" , Cambridge Univ. Press (1927)