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With $i^2=-1$, what is $i!$ ?

I'm not sure if it is $i$ or if it is an infinite product $i(i-1)(i-2)(i-3)(i-4)(i-5)\dots$

It would make sense either way.

Is it not defined?

Hippalectryon
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Phi i Mathematical Pi
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    Have you heard about the Gamma function? It is the usual way of interpreting factorials for general complex numbers. For instance WolframAlpha interprets $i!$ as $\Gamma(i + 1)$. – Arthur Nov 10 '14 at 23:23
  • Yes I would say look into the gamma function as it probably holds the key to your problem. It can be represented as an infinite product or as an integral. It can also pop out in other situations... – bjd2385 Nov 10 '14 at 23:29

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Check out http://en.wikipedia.org/wiki/Gamma_function

$$\Gamma(i+1) \approx 0.498015668 - 0.154949828\, i $$

orangeskid
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