A Note on a Fourier Sine Transform
This is a compilation of definite integrals of the product of the hyperbolic cosecant function and polynomial raised to a general power. In this work, we used our contour integral method to derive a Fourier sine transform in terms of the Lerch function. Almost all Lerch functions have an asymmetrica...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/13/10/1828 |
| _version_ | 1797513120913031168 |
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| author | Robert Reynolds Allan Stauffer |
| author_facet | Robert Reynolds Allan Stauffer |
| author_sort | Robert Reynolds |
| collection | DOAJ |
| description | This is a compilation of definite integrals of the product of the hyperbolic cosecant function and polynomial raised to a general power. In this work, we used our contour integral method to derive a Fourier sine transform in terms of the Lerch function. Almost all Lerch functions have an asymmetrical zero-distribution. A summary table of the results are produced for easy reading. A vast majority of the results are new. |
| first_indexed | 2024-03-10T06:10:17Z |
| format | Article |
| id | doaj.art-3ddf10b2637c48df82c6fe4c812cf1db |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T06:10:17Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-3ddf10b2637c48df82c6fe4c812cf1db2023-11-22T20:09:42ZengMDPI AGSymmetry2073-89942021-09-011310182810.3390/sym13101828A Note on a Fourier Sine TransformRobert Reynolds0Allan Stauffer1Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, CanadaDepartment of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, CanadaThis is a compilation of definite integrals of the product of the hyperbolic cosecant function and polynomial raised to a general power. In this work, we used our contour integral method to derive a Fourier sine transform in terms of the Lerch function. Almost all Lerch functions have an asymmetrical zero-distribution. A summary table of the results are produced for easy reading. A vast majority of the results are new.https://www.mdpi.com/2073-8994/13/10/1828entries in Gradshteyn and Ryzhikdefinite integralcontour integral |
| spellingShingle | Robert Reynolds Allan Stauffer A Note on a Fourier Sine Transform Symmetry entries in Gradshteyn and Ryzhik definite integral contour integral |
| title | A Note on a Fourier Sine Transform |
| title_full | A Note on a Fourier Sine Transform |
| title_fullStr | A Note on a Fourier Sine Transform |
| title_full_unstemmed | A Note on a Fourier Sine Transform |
| title_short | A Note on a Fourier Sine Transform |
| title_sort | note on a fourier sine transform |
| topic | entries in Gradshteyn and Ryzhik definite integral contour integral |
| url | https://www.mdpi.com/2073-8994/13/10/1828 |
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