Extended Mellin integral representations for the absolute value of the gamma function
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...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2018
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/89152 http://hdl.handle.net/10220/44811 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Nanyang Technological University |
| Language: | English |
| id |
sg-ntu-dr.10356-89152 |
|---|---|
| record_format |
dspace |
| spelling |
sg-ntu-dr.10356-891522023-02-28T19:35:36Z Extended Mellin integral representations for the absolute value of the gamma function Privault, Nicolas School of Physical and Mathematical Sciences Mellin Transform Gamma Function 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. MOE (Min. of Education, S’pore) Published version 2018-05-17T01:37:42Z 2019-12-06T17:19:02Z 2018-05-17T01:37:42Z 2019-12-06T17:19:02Z 2018 Journal Article Privault, N. (2018). Extended Mellin integral representations for the absolute value of the gamma function. Analysis, 38(1), 11-20. 0174-4747 https://hdl.handle.net/10356/89152 http://hdl.handle.net/10220/44811 10.1515/anly-2017-0046 en Analysis © 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: [http://dx.doi.org/10.1515/anly-2017-0046]. 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. 10 p. application/pdf |
| institution |
Nanyang Technological University |
| building |
NTU Library |
| continent |
Asia |
| country |
Singapore Singapore |
| content_provider |
NTU Library |
| collection |
DR-NTU |
| language |
English |
| topic |
Mellin Transform Gamma Function |
| spellingShingle |
Mellin Transform Gamma Function Privault, Nicolas Extended Mellin integral representations for the absolute value of the gamma function |
| description |
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. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Privault, Nicolas |
| format |
Article |
| author |
Privault, Nicolas |
| author_sort |
Privault, Nicolas |
| title |
Extended Mellin integral representations for the absolute value of the gamma function |
| title_short |
Extended Mellin integral representations for the absolute value of the gamma function |
| title_full |
Extended Mellin integral representations for the absolute value of the gamma function |
| title_fullStr |
Extended Mellin integral representations for the absolute value of the gamma function |
| title_full_unstemmed |
Extended Mellin integral representations for the absolute value of the gamma function |
| title_sort |
extended mellin integral representations for the absolute value of the gamma function |
| publishDate |
2018 |
| url |
https://hdl.handle.net/10356/89152 http://hdl.handle.net/10220/44811 |
| _version_ |
1759857621817360384 |