A definition of the gamma function due to Carl Friedrich Gauss that is valid for all real

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A definition of the gamma function due to Carl Friedrich Gauss that is valid for all real numbers, except x = 0, -1, -2, ...,  is given by

n!n* I(x) = lim x(x + 1)(x + 2).. (x + n)


Use this definition to show that Γ(x + 1) = xΓ(x).

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