Definition and properties of the Gamma function

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See https://math.libretexts.org/Bookshelves/Analysis/Complex_Variables_with_Applications_(Orloff)/14%3A_Analytic_Continuation_and_the_Gamma_Function/14.02%3A_Definition_and_properties_of_the_Gamma_function

How to prove Legendre duplication formula?

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Jianzhihu https://www.zhihu.com/question/403116146

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