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Kronecker delta simplification involving fractions?

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Hi guys, how are you all doing? I hope that you are all doing fine!

So, I just started to make use of Mathematica few months ago, therefore I dont know if it's a silly question. I have the following the kind of term to be simplified

Sum[{A[l, l1, i, j, k, l]/B[j, j + 1, i, j]} KroneckerDelta[i, l], {i, 0, \[Infinity]}]

However, looks like that Mathematica is not able to solve it. It just returns the same expression. But, if I change the Kronecker delta argument to [i,10], instead of [i,l], the sum is simplified.

I'd like to know if there's a way to simplify this kind of expression, since it does simplify this kind of sum, if there is no fraction. I mean:

Sum[A[l, l1, i, j, k, l] KroneckerDelta[i, l], {i, 0, \[Infinity]}]
POSTED BY: Vinicius Henning
Answer
2 months ago

Wrap your sum in Assuming[Element[l, Integers], expr], for example:

Assuming[
   Element[l, Integers],
   Sum[{A[l, l1, i, j, k, l]/B[j, j + 1, i, j]} KroneckerDelta[i, l], {i, 0, \[Infinity]}]
] //InputForm

(* {Piecewise[{{A[l, l1, l, j, k, l]/B[j, 1 + j, l, j], l >= 0}}, 0]} *)
POSTED BY: Carl Woll
Answer
2 months ago

That works! Thanks Carl! But it's funny, because I've used assuming already, but I added an extra info, that l >= 0, and for this case Mathematica just don't solve it. Do you know if is there anything else "behind the scenes", that I'm not seeing? I'm trying some stuffs here, but I'm not get a solution

Thanks again!

POSTED BY: Vinicius Henning
Answer
2 months ago

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