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The following tabulates the various appearances of the multiplication theorem for finite characteristic; the characteristic zero relations are given further down. In all cases, ''n'' and ''k'' are non-negative integers. For the special case of ''n'' = 2, the theorem is commonly referred to as the '''duplication formula'''.
==Gamma
The duplication formula and the multiplication theorem for the [[gamma function]] are the prototypical examples. The duplication formula for the gamma function is
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