Is it true that [tex] \sum_x e^{i(k-k')x} = \delta_{k-k'} [/tex], where [tex]\delta[/tex] is the Kronecker delta? I've come across a similar relation for the Dirac Delta (when the sum is an integral). I do not understand why [tex]k-k' \neq 0 [/tex] implies the sum is zero.(adsbygoogle = window.adsbygoogle || []).push({});

Edit: In fact, I'm really confused, since it seems that when the [tex]x=0...\inf[/tex] and k=k' the sum is infinite. So is it a Dirac delta?

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# Definition of Delta as a Sum

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