Closed form for sum of x^i divided by (i!)^2

[jacobcdf]

Hi all,

I've been messing around with the product of Poisson distributions and was hoping someone could help me work out a closed form solution for the following convergent infinite series (given x > 0):

$$\sum^{\infty}_{i=0}$$ $$\frac{x^{i}}{i! \times i!}$$​

Many thanks in advance,
Jacob.

 

[ice109]

$$I_0\left(2 \sqrt{x}\right)$$

which is the modified bessel function of the first kind

 

[jacobcdf]

$$I_0\left(2 \sqrt{x}\right)$$

which is the modified bessel function of the first kind

Muchos gracias, amigo. That helps a lot. :)

Although now that I think about I should have been able to intuit that one on my own. I'm just getting old I guess. :(