Weyrich's Formula

Under appropriate constraints,

${1\over 2} i \int_{-\infty}^\infty H_0^{(1)}(r\sqrt{k^2-r^2}\,)e^{i\tau x} \,d\tau = {e^{ik\sqrt{r^2+k^2}}\over\sqrt{r^2+x^2}},$

where $H_0^{(1)}(z)$ is a Hankel Function of the First Kind.

References

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1474, 1980.