“…There exists a very extensive literature on the gamma function. In particular, numerous remarkable inequalities involving Γ and its logarithmic derivative ψ = Γ /Γ have been published by different authors; see, e.g., [2], [3], [6], [7], [9], [12], [13], [18]- [27], [29]- [33], [35]- [46], [50]. Many of these inequalities follow immediately from the monotonicity properties of functions which are closely related to Γ and ψ.…”