sums of Bessel functions

From: Zbyszek (chytrus_at_o2.pl)
Date: 11/20/04 

Date: Sat, 20 Nov 2004 14:52:07 +0100

I've got a problem with sums of modified bessel functions I_k(t)
I need to have sth. like this

sum_{k=0}^ \infty ( a^k * I_k (t) )

I know that

sum_{k= - \infty}^ \infty ( a^k * I_k (t) )=exp( t/2 (a+1/a) )

but I need sum that starts from k=0.

Thanks for any clues.
Zbyszek.

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