Lipschitz's Integral

$$\int_0^\infty e^{-ax} J_0(bx)\,dx = {1\over\sqrt{a^2+b^2}},$$

where $J_0(z)$ is the zeroth order Bessel Function of the First Kind.

References

Bowman, F. Introduction to Bessel Functions. New York: Dover, p. 58, 1958.