Sub- and Superadditive Properties of Euler’s Gamma Function
نویسنده
چکیده
Let α > 0 and 0 < c = 1 be real numbers. The inequality (Γ(x+ y + c) Γ(x+ y) )1/α < (Γ(x+ c) Γ(x) )1/α + (Γ(y + c) Γ(y) )1/α holds for all positive real numbers x, y if and only if α ≥ max(1, c). The reverse inequality is valid for all x, y > 0 if and only if α ≤ min(1, c).
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تاریخ انتشار 2007