Can I more simply express this summation?

Asked Apr 12 '17 at 07:36

Active Apr 12 '17 at 07:41

Viewed 44 times

I've been trying to make the below equation more simple such like binomial theorem: $\sum^{n}_{i=0} \binom ni a^ib^{n-i}=(a+b)^n$.

The equation I want to make more simple is : $\sum^{n-1}_{i=0} \binom ni i! x^{-i}$.

Does anybody have any idea to simplify it?

Thanks in advance for your help.

edited Apr 12 '17 at 07:41

E. Joseph

asked Apr 12 '17 at 07:36

hoesang choi

The expression simplifies if you're allowed access to the incomplete gamma function, but that's basically just rephrasing the sum. – Patrick Stevens Apr 12 '17 at 07:39
Thanks a lot. The incomplete gamma function is very useful for me! – hoesang choi Apr 12 '17 at 11:48

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