I want to transform the expression x*y*Inactive[Sum][1/n^2,{n,1,Infinity}] to the expression Inactive[Sum][x*y/n^2,{n,1,Infinity}] with the symbolic function Distribute :
Distribute[x*y*Inactive[Sum][1/n^2,{n,1,Infinity}],Inactive[Sum],Times]
But this does not work. I get the answer
Inactive[Sum][x*y/n^2,{x*y*n,x*y,x*y*Infinity}]
What can I do to solve this problem or is this a bug in Mathematica?
It’s distributing across all positions, as it should. If it were inconsistent in this regard, that would be a (serious) bug.
I believe a common approach to this is to use a replacement rule. I am not on a machine with Mathematica at the moment, but something like the following.
x*y*Inactive[Sum][1/n^2,{n,1,Infinity}] /. a_. * Inactive[Sum][b_,c__] :> Inactive[Sum][a*b,c]
In[5]:= xyInactive[Sum][1/n^2, {n, 1, Infinity}] /.
a_.Inactive[Sum][b_, c__] :> Inactive[Sum][ab, c]
Out[5]= Inactive[Sum][(x y)/n^2, {n, 1, \[Infinity]}]