Whittaker transform

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The integral transform


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.


[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)
How to Cite This Entry:
Whittaker transform. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by Yu.A. BrychkovA.P. Prudnikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article