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D under Sum


Hello

I want the derivation D to be applied under the Sum sign,
I have a function HoldSum that do not evaluate but is similar to Sum in form

In[3]:= D[HoldSum[p*i, {i, 1, n}], p]

I get the output :

Out[3]=i*HoldSum^(1, {0, 0, 0})[i p, {i, 1, n}]

but I would want that D be applied under the Sum sign like done by hand here :

In[5]:= HoldSum[D[p i, i], {i, 1, n}]

Out[5]= HoldSum[p, {i, 1, n}]

Obviously I want D to work for any expression containing HoldSum (even on nested HoldSum expression)

Does anybody knows how to do that ?

Best regards

Nicolas



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