kron[m_,n_]:=\!\((adsbygoogle = window.adsbygoogle || []).push({});

\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2\)]\(\(Sin[

\*FractionBox[\(n\ \[Pi]\ x\), \(2\)]]\ Sin[

\*FractionBox[\(m\ \[Pi]\ x\), \(2\)]]\) \[DifferentialD]x\)\)

This is the integral over x of sin(n pi x / 2) times sin(m pi x / 2) from 0 to 2. This is one way to define the Kronecker Delta function. Given m and n as integers and not both zero, if m = n then the output is 1, if m ≠ n the output is 0.

Why then is it that when I type:

Simplify[kron[m, n],

Element[m, Integers] && Element[n, Integers]]

that I get zero?

If I do kron[1, 1] I get 1! How can Mathematica say a function is 0 over the integers when I just put in two integers and got a non-zero ouput?

It is certainly not identical to zero right?

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# Form of Kronecker Delta Not Recognized in Mathematica

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