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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

4 votes
1 answer
353 views

Proving two inequalities involving the gamma and digamma functions

I'm having trouble proving the following inequality: $$\forall p>1 \quad \forall m\geq 0 \quad \dfrac{m^2\Gamma(\dfrac{2m}{p})\Gamma(\dfrac{2m}{q})}{\Gamma(\dfrac{2m+2}{p})\Gamma(\dfrac{2m+2}{q})}\ge …