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On the Horizontal Monotonicity of |Γ(s)|

Published online by Cambridge University Press:  20 November 2018

Gopala Krishna Srinivasan  and
P. Zvengrowski
Gopala Krishna Srinivasan
Affiliation:
Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India e-mail: gopal@math.iitb.ac.in
P. Zvengrowski
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4 e-mail: zvengrow@ucalgary.ca
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Abstract

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Writing $s\,=\,\sigma \,+\,it$ for a complex variable, it is proved that the modulus of the gamma function, $\left| \Gamma (s) \right|$, is strictly monotone increasing with respect to $\sigma $ whenever $\left| t \right|\,>\,5/4$. It is also shown that this result is false for $\left| t \right|\,\le \,1$.

Keywords

33B15Gamma functionmodulusmonotonicity
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 3 , 01 September 2011 , pp. 538 - 543
Copyright
Copyright © Canadian Mathematical Society 2011

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