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Old 2020-05-10, 06:11   #6
Batalov's Avatar
Mar 2008

22·2,333 Posts

Originally Posted by retina View Post
Presumably n! = Γ(n + 1). For n >= 0 that would suffice, right? What did I miss?
You are missing that n! = Γ(n+1) + sin(πn). Or Γ(n+1) + sin(π(n+1)); take your pick... Wikipedia is helpful to demonstrate that both are valid analytic continuations of the factorials to the non-integers.
Do Γ(n+1) and Γ(n+1) + sin(πn) have the same derivatives?
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