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# On the Horizontal Monotonicity of $|\Gamma(s)|$

Published:2010-12-31
Printed: Sep 2011
• Gopala Krishna Srinivasan,
Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
• P. Zvengrowski,
Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4
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## Abstract

Writing $s = \sigma + it$ for a complex variable, it is proved that the modulus of the gamma function, $|\Gamma(s)|$, is strictly monotone increasing with respect to $\sigma$ whenever $|t| > 5/4$. It is also shown that this result is false for $|t| \leq 1$.
 Keywords: Gamma function, modulus, monotonicity
 MSC Classifications: 33B15 - Gamma, beta and polygamma functions

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