  We derive integral representations in terms of the Macdonald functions for
the square modulus $s\mapsto | \Gamma ( a + i s ) |^2$ 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.
