- #1

Ted123

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## Homework Statement

I've got to show [tex]\sum_{n=0}^{\infty} \frac{(a)_n(-1)_n}{(c)_n n!} = \frac{c-a}{c}[/tex]

where

[tex]\displaystyle (a)_n = \frac{\Gamma(a+n)}{\Gamma(a)} = a(a+1)...(a+n-1)[/tex]

is the shifted factorial (Pochhammer symbol).

## The Attempt at a Solution

I've been informed that [tex](-1)_n = 0\;\;\;\;\;\;\forall\;\;n\geq 2[/tex]

So the sum has only 2 terms for n=0 and n=1, but what do e.g. [tex](-1)_0\,,\,(-1)_1\,,\,(a)_0\,,\,(a)_1[/tex] equal?