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How to obtain the power series of finite power sum?

GROUPS:
Is there anybody can help me to get an expansion for the following finite Power Sum?
(Sum[(\[Beta]*x)^i/i!, {i, 0, m - 1}])^n
As I know the infinite power sum can be expressed as follows


but what about the case of finite power sum? 

Thanks for your support
POSTED BY: Yahia Alghorani
Answer
4 months ago
I get the following result using Mathematica 9:

In[1]:= (Sum[(\[Beta]*x)^i/i!, {i, 0, m - 1}])^n


Out[1]= ((E^(x \[Beta]) Gamma[m, x \[Beta]])/Gamma[m])^n

S M Blinder
POSTED BY: S M Blinder
Answer
4 months ago
Thanks for your reply, but I need to get a result in summation form, and Not in Gamma function. 
POSTED BY: Yahia Alghorani
Answer
4 months ago