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I was wondering if there are any results that studied the growth of $\left|\frac{1}{\Gamma(s)}\right|$ where $0 < \Re(s) < 1$ and as $\Im(s) \to \infty$? Any pointers to any results, papers, references will be highly appreciated.


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up vote 5 down vote accepted

According to Gradshteyn-Ryzhik: Tables of integrals... 8.328.1, for fixed real $x$ and for $|y|\to\infty$ one has $$ |\Gamma(x+iy)|\sim\sqrt{2\pi}e^{-\frac\pi 2|y|}|y|^{x-\frac12}. $$

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And in general, Stirling formula (asymptotic expansion) holds as $|z|\to\infty$ uniformly with respect to $\arg z$ in every angle of the form $|\arg z|<\pi-\epsilon,\; \epsilon>0$. – Alexandre Eremenko Apr 20 '13 at 13:27
anton,Alexandre Thanks! :) – Roupam Ghosh Apr 21 '13 at 2:37

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