I'm having trouble getting Mathematica (, OSX High Sierra) to evaluate the following sum:

$\sum_{i=0}^{\infty} f(i) \, g(i) \, \delta_{i,j}$

My code is

Sum[f[i] g[i] KroneckerDelta[i, j], {i, 0, Infinity}]

The output I was expecting was

f[j] g[j] UnitStep[j]

but instead I get the original sum. When I remove f[i] or g[i] from the expression, however, I get the expected result.


1 Answer 1


Try using assumptions:

    j ∈ Integers && j >= 0,
    Sum[f[i] g[i] KroneckerDelta[i, j], {i, 0, Infinity}]

f[j] g[j]

  • 1
    $\begingroup$ Hmm, that doesn't seem to work -- I just get the sum back. $\endgroup$ Feb 24, 2018 at 3:00
  • $\begingroup$ @RichardTownsend Seems like this was improved in M11.2. $\endgroup$
    – Carl Woll
    Feb 24, 2018 at 3:03
  • $\begingroup$ Unfortunately, my University site licence appears to be stuck at I'll have to find out what the plans are for updating it. But in the meantime, many thanks for the quick response. $\endgroup$ Feb 24, 2018 at 3:08
  • $\begingroup$ Ok, managed to upgrade to 11.2, and your solution works perfectly. Many thanks again, Carl! $\endgroup$ Feb 24, 2018 at 3:58

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