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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 Gamma function, modulus, monotonicity
MSC Classifications: 33B15 show english descriptions Gamma, beta and polygamma functions 33B15 - Gamma, beta and polygamma functions
 

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