Laplace Transform of Bessel Function of the First Kind of Order One

Theorem
Let $J_1$ denote the Bessel function of the first kind of order $1$.

Then the Laplace transform of $J_1$ is given as:


 * $\laptrans {\map {J_1} t} = \dfrac {\sqrt {s^2 + 1} - s} {\sqrt {s^2 + 1} }$