Prove that:
$j_0(\sqrt{x^2-2xt})=\sum_{n=0}^{\infty}\dfrac{t^n}{n!}j_n(x)$
the result can be obtained by applying the Taylor expansion for a conveniently chosen function, with appropriate changes of variable, and the help from
$j_n(x)=(-1)^nx^n\left(\dfrac{1}{x}\dfrac{d}{dx} \right)^n\left( \dfrac{\sin(x)}{x} \right)$
I think it can be obtained from the generating function for spherical Bessel functions, but I can't find a way to relate it.