Closed-Form Solution Desired for Infinite Series

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stevendaryl
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Is there a simple closed-form solution for the following infinite series?

##F(a,b,c) = \sum_{j=0}^\infty \frac{(j+a)!}{(j+b)! (j+c)!}##

where ##a, b, c## are positive integers?
 

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  • #2
haruspex
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Is there a simple closed-form solution for the following infinite series?

##F(a,b,c) = \sum_{j=0}^\infty \frac{(j+a)!}{(j+b)! (j+c)!}##

where ##a, b, c## are positive integers?
In the simple special case of a=b, that will give ##e- \sum_{j=0}^{c-1} \frac 1 {j!}##, no?
I would not count that as closed form.
 
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