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Help with infinite series sum{i=0=>inf} (x^i / (i!)^2)

  1. Jun 9, 2010 #1
    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):

    [tex]\sum^{\infty}_{i=0}[/tex] [tex]\frac{x^{i}}{i! \times i!}[/tex]​

    Many thanks in advance,
  2. jcsd
  3. Jun 9, 2010 #2
    [tex]I_0\left(2 \sqrt{x}\right)[/tex]

    which is the modified bessel function of the first kind
  4. Jun 9, 2010 #3
    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. :(
    Last edited: Jun 9, 2010
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