Modified Bessel Function of the 1st Kind

A series expansion for the order zero, modified Bessel function of the first kind is given by

$$I_0(x) = \sum_{k=0}^{\infty} \left[ \frac{(x/2)^k}{k!} \right]^2$$

Compare this with

$$e^{x/2} = \sum_{k=0}^{\infty}\frac{(x/2)^k}{k!}.$$