Summation of Reciprocal of Zero of Order 1 Bessel Function by Order 0 Bessel Function of it

Theorem

 * $\displaystyle \sum_{n \mathop = 1}^\infty \dfrac 1 {x_n \map {J_0 } {x_n} } = 0 \cdotp 38479 \ldots$

where:
 * $x_n$ is the $n$th zero of the order $1$ Bessel function of the first kind
 * $\map {J_0 } {x_n}$ is the order $0$ Bessel function of the first kind of $x_n$.