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for integer ''k'' ≥ 1, and is sometimes called '''Gauss's multiplication formula''', in honour of [[Carl Friedrich Gauss]]. The multiplication theorem for the gamma functions can be understood to be a special case, for the [[trivial character]], of the [[Chowla–Selberg formula]].
==Polygamma function, harmonic numbers==
The [[polygamma function]] is the [[logarithmic derivative]] of the gamma function, and thus, the multiplication theorem becomes additive, instead of multiplicative:
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:<math>k\left[\psi(kz)-\log(k)\right] = \sum_{n=0}^{k-1}
\psi\left(z+\frac{n}{k}\right).</math>
The polygamma identities can be used to obtain a multiplication theorem for [[harmonic number]]s.
==Hurwitz zeta function==
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