What is the $\mathcal Z$-transform of Bessel function $J_0(\alpha n)$ sequence
The Taylor expansion for the Bessel function of the first kind and 0th order is 
$$
J_{0}\left ( x \right )= \sum_{m=0}^{\infty }\frac{(-1)^{m}}{(m!)^{^{2}}}\left ( \frac{1}{2}x \right )^{2m}
$$

(see http://en.wikipedia.org/wiki/Bessel_function)

So you can basically approximate this as the Z-transform of a polynomial.