Mehler's Bessel Function Formula

$$J_0(x)={2\over\pi}\int_0^\infty \sin(x\cosh t)\,dt,$$

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

References

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1472, 1980.