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Kronecker's delta symbol

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kroneckerDelta(m, <n>)


kroneckerDelta(m, n) is Kronecker's delta symbol. It represents 1 if m = n and 0 if mn.

kroneckerDelta(m) represents 1 if m = 0 and 0 if m ≠ 0.

The calls kroneckerDelta(m, n) and kroneckerDelta(m - n) are equivalent.

kroneckerDelta(m, n) yields 1 if the arguments m, n coincide.

It yields 0 if m - n yields a non-zero numerical value.

If either m or n contain symbolic objects and m - n does not yield a numerical value, then the symbolic call kroneckerDelta(m, n) or the equivalent call kroneckerDelta(n, m) is returned.

Floating point numbers such as 1.0, 2.0 etc. are treated like integers.

Note that kroneckerDelta(m,n) = kroneckerDelta(n,m) for arbitary arguments m, n. In symbolic return values, the ordering of the input arguments may be exchanged.

kroneckerDelta is used and processed by sum and ztrans, iztrans.


Example 1

kroneckerDelta returns 1 or 0, respectively, for arguments that definitely coincide or do not coincide:

kroneckerDelta(2, 2), kroneckerDelta(n, n),
kroneckerDelta(2, 3), kroneckerDelta(n - 1, n + 1)

A symbolic call is returned if the system cannot decide whether the arguments coincide:

kroneckerDelta(m, n), kroneckerDelta(m, 3), kroneckerDelta(3, n)

Example 2

kroneckerDelta is processed by sum:

sum(a[n]*kroneckerDelta(n, 3), n = 0..infinity)

sum(a[n]*kroneckerDelta(n, m), n = 0..infinity)

iztrans may produce terms involving kroneckerDelta:

iztrans(1/(z - 1), z, n)

ztrans(%, n, z)


m, n

arithmetical expressions. The default value for n is 0.

Return Values

Arithmetical expression.

Overloaded By

m, n

See Also

MuPAD Functions

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