Extended Mellin integral representations for the absolute value of the gamma function - Privault, Nicolas (2018)
We derive Mellin integral representations in terms of Macdonald functions for the squared absolute value s↦|Γ(a+is)|2 of the gamma function and its Fourier transform when a<0 is non-integer, 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 a Fokker–Planck equation.