sum simplification

Question

I have this sum

 Sum[-E^(-j (x kx[p] + y ky[q] + z kz[r])) j g w ky[q] Ux[p, q, r],
     {p, -∞, ∞}, {q, -∞, ∞}, {r, -∞, ∞}]

and I would like to pull constants out of the triple sum. I have so many terms that is why I prefer to do it automatic.

Thanks in advance

Answer 1

This is kind of ugly, but here goes:

factorFromSum[sum_, vars_] :=
    Inactivate[sum, Sum] /.
      Inactive[Sum][Times[a_, rest_?(Function[{pat}, AllTrue[FreeQ[pat, #] &]@vars])], r___]
      :>
      rest Inactive[Sum][a, r]
SetAttributes[factorFromSum, HoldFirst];

Example:

factorFromSum[Sum[5 x^2, {x, 1, 10}], {x}]

outputs

5 Inactive[Sum][x^2, {x, 1, 10}]

To reenable the sum, finally perform Activate[#, Sum]&.

Your final output is given by

factorFromSum[
  Sum[-E^(-j (x kx[p] + y ky[q] + z kz[r])) j g w ky[q] Ux[p, q, r],
     {p, -Infinity, Infinity},
     {q, -Infinity, Infinity},
     {r, -Infinity, Infinity}],
  {p, q, r}]
// Activate[#, Sum]&