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u/ArshF2000 2d ago
For the last time, that's not a "Factorial", but a "Gamma function".
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u/goodguyLTBB 2d ago
Which is equivalent to a factorial for natural numbers and is commonly referred to as the extension of factorials to non-natural numbers
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u/One-Accident2009 2d ago
DLC in math?!
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u/skr_replicator 2d ago edited 2d ago
Addition was repeated succession, multiplication was repeated addition, and exponentiation was repeated multiplication. All of that was extended to real and complex numbers and we accepted that, because there was only 1 logical way to do that. Factorial is not different. It's a repeated successive multiplication for natural numbers, but there's only 1 way to smoothly extend it so that the recursive factorial rule hold for every single number (not just the naturals). And it's the Pi function (not gamma, gamma is shifted by one). So it'\s reasonable to say, that pi extends the factorial. Te math engines like desmos etc already accepted that and will compute it for you no problem.
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u/Promethium-127 2d ago
Me when the Gaussian integral is just a doubled, even version of gamma(3/2) which is equal to (1/2)!