A result regarding monotonicity of the Gamma function

Pál A. Kupán; Gyöngyvér Márton; Róbert Szász

doi:10.1515/ausm-2017-0022

Abstract

In this paper we analyze the monotony of the function $\frac{ln Γ (x)}{ln (x^{2} + τ) - ln (x + τ)}$ ${{{\rm{ln}}\,\Gamma ({\rm{x}})} \over {{\rm{ln}}\,({\rm{x}}^2 + \tau) - {\rm{ln}}\,({\rm{x}} + \tau)}}$ , for τ > 0. Such functions have been used from different authors to obtain inequalities concerning the gamma function.

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A result regarding monotonicity of the Gamma function

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