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Title: Extended Mellin integral representations for the absolute value of the gamma function
Authors: Privault, Nicolas
Keywords: Mellin Transform
Gamma Function
Issue Date: 2018
Source: Privault, N. (2018). Extended Mellin integral representations for the absolute value of the gamma function. Analysis, 38(1), 11-20.
Series/Report no.: Analysis
Abstract: 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.
ISSN: 0174-4747
DOI: 10.1515/anly-2017-0046
Rights: © 2018 Walter de Gruyter GmbH, Berlin/Boston. This paper was published in Analysis and is made available as an electronic reprint (preprint) with permission of Walter de Gruyter GmbH, Berlin/Boston. The published version is available at: []. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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