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arXiv · 1410.5043

On the integral representations of $|Γ(z)|^2$ and its Fourier transform

Nicolas Privault
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Abstract

We derive integral representations in terms of the Macdonald functions for the square modulus $s\mapsto | Γ( a + i s ) |^2$ of the Gamma function and its Fourier transform when $a<0$ and $a\not= -1,-2,\ldots $, generalizing known results in the case $a>0$. This representation is based on a renormalization argument using modified Bessel functions of the second kind, and it applies to the representation of the solutions of the Fokker-Planck equation.

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Nicolas Privault. 2014-10-19. On the integral representations of $|Γ(z)|^2$ and its Fourier transform. https://arxiv.org/abs/1410.5043

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