Whittaker transform

The integral transform

$$F(x)=\underset{0}{\overset{\mathrm{\infty }}{\int }}(2xt{)}^{-1/4}{W}_{\lambda ,\mu }(2xt)f(t)dt,$$

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

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