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Question: Summation in different form

Question:Summation in different form

schzan 130
sum physics summation
September 11 2015
3

Dear Feinds,

How can I compute a double summation of the following form in Maple.

                                                      ∑5m=1  ∑j+k=m-1 (2m (Dk(a_m*f)) (Dj(f)))

where Dn represents nth order derivative.

Thank you for your help!

EDIT 1

Summand added

EDIT 2

Function "f" in the first derivative is changed to "a_m*f" where a_m (variable coefficients) represents any function of x.

First of all thank you so much for all the nice answers.

Here, the notation a_m doesn't work as I was expecting and then I thought let's just make it a(m) for simplicity, it seemed to work fine but unfortunately D assumes it as a constant function. How can I rectify this problem?

 
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