<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we analyze the monotony of the function 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2017-0022_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mrow><mtext>ln</mtext><mi> </mi><mi>Γ</mi><mo>(</mo><mtext>x</mtext><mo>)</mo></mrow><mrow><mtext>ln</mtext><mi> </mi><mo>(</mo><msup><mtext>x</mtext><mn>2</mn></msup><mo>+</mo><mi>τ</mi><mo>)</mo><mo>-</mo><mtext>ln</mtext><mi> </mi><mo>(</mo><mtext>x</mtext><mo>+</mo><mi>τ</mi><mo>)</mo></mrow></mfrac></mrow></math><tex-math>${{{\rm{ln}}\,\Gamma ({\rm{x}})} \over {{\rm{ln}}\,({\rm{x}}^2 + \tau) - {\rm{ln}}\,({\rm{x}} + \tau)}}$</tex-math></alternatives></inline-formula>
, for τ > 0. Such functions have been used from different authors to obtain inequalities concerning the gamma function.</p></abstract>

In this paper we analyze the monotony of the function 
ln Γ(x)ln (x2+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.

A result regarding monotonicity of the Gamma function

Department of Mathematics-Informatics, Faculty of Technical and Human, Sciences

Sapientia Hungarian University of Transylvania

Department of Mathematics-Informatics, Faculty of Technical and Human Sciences

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"A result regarding monotonicity of the Gamma function"}

In this paper we analyze the monotony of the function 
ln Γ(x)ln (x2+τ)-ln (x+τ)${{{\rm{ln}}\,\Gamma ({\rm{x}})} \over {{\rm{ln}}\,({\rm{x}}^2 + \tau) -...

A result regarding monotonicity of the Gamma function

Published Online: Mar 07, 2018

Page range: 291 - 302

Received: Oct 15, 2017

DOI: https://doi.org/10.1515/ausm-2017-0022

Keywords
Gamma function, monotonic function

© 2017 Pál A. Kupán et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A result regarding monotonicity of the Gamma function

Published Online: Mar 07, 2018

Page range: 291 - 302

Received: Oct 15, 2017

DOI: https://doi.org/10.1515/ausm-2017-0022

KeywordsGamma function, monotonic function

© 2017 Pál A. Kupán et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Gamma function, monotonic function