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On the Horizontal Monotonicity of |Γ(s)|
Published online by Cambridge University Press: 20 November 2018
Abstract
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 $\left| t \right|\,\le \,1$.
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- Copyright © Canadian Mathematical Society 2011
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