Asymptotic expansion of Bessel function of the first kind, order zero

Question

What would the asymptotic expansion of the following Bessel function look like?

$$J_0(2i\sqrt{x})$$

There are examples that show that the result is

$$1+x+\frac{x^2}{(2!)^2}+\frac{x^3}{(3!)^2}+...,$$

but these do not give the solution procedure.