A result regarding monotonicity of the Gamma function
A result regarding monotonicity of the Gamma function
Abstract In this paper we analyze the monotony of the function <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mfrac> <m:mrow> <m:mtext>ln</m:mtext> <m:mi> </m:mi> <m:mi>Γ</m:mi> <m:mo>(</m:mo> <m:mtext>x</m:mtext> <m:mo>)</m:mo> </m:mrow> <m:mrow> <m:mtext>ln</m:mtext> <m:mi> </m:mi> <m:mo>(</m:mo> <m:msup> <m:mtext>x</m:mtext> <m:mn>2</m:mn> </m:msup> <m:mo>+</m:mo> <m:mi>τ</m:mi> <m:mo>)</m:mo> <m:mo>-</m:mo> <m:mtext>ln</m:mtext> <m:mi> </m:mi> <m:mo>(</m:mo> <m:mtext>x</m:mtext> <m:mo>+</m:mo> <m:mi>τ</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mfrac> </m:mrow> </m:math> ${{{\rm{ln}}\,\Gamma …