0^n

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With

n

a real number, we have
     

0 n = ⎧   ⎨   ⎩     ∞  if n   <   0, 1  if n   =   0, 0  if n   >   0.

Note that for 0 0 we have the empty product, i.e. 1.

A000007 The characteristic function of 0:

a (n) = 0 n, n   ≥   0

.

{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...}

See also

• Univariate Kronecker delta
• 0 0
• Characteristic functions