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The factorial function: convex functions, the Bohr-Mollerup-Artin theorem, and some formulae
Published online by Cambridge University Press: 01 August 2016
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How might we define x!? This is the next in my series of articles [1-3]; by now we know quite a bit about the factorial function, except that we have no real definition of it, nothing that would allow us to evaluate, say, ½!. So how do we move on to the next stage?
There is a range of strategies. We could find or manufacture a suitable function f that satisfies the basic relations
and adopt it as our definition.
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References
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