- #1

euphoricrhino

- 22

- 7

While reading Sakurai (scattering theory/Eikonal approximation section), I encountered a referenced integral

##

\int_0^\infty J_1(x)^2\frac{dx}{x}=1/2

##

I also see this integral from a few places (wolfram, DLMF, etc), so I tried to prove this from various angles (recurrence relations, series representation of J_n, etc) but have not succeeded.

Can anyone provide a sketch of the proof?

Thanks!