A Note on the Summation of the Incomplete Gamma Function
We examine the improved infinite sum of the incomplete gamma function for large values of the parameters involved. We also evaluate the infinite sum and equivalent Hurwitz-Lerch zeta function at special values and produce a table of results for easy reading. Almost all Hurwitz-Lerch zeta functions h...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/12/2369 |
| _version_ | 1797500289621688320 |
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| author | Robert Reynolds Allan Stauffer |
| author_facet | Robert Reynolds Allan Stauffer |
| author_sort | Robert Reynolds |
| collection | DOAJ |
| description | We examine the improved infinite sum of the incomplete gamma function for large values of the parameters involved. We also evaluate the infinite sum and equivalent Hurwitz-Lerch zeta function at special values and produce a table of results for easy reading. Almost all Hurwitz-Lerch zeta functions have an asymmetrical zero distribution. |
| first_indexed | 2024-03-10T03:59:46Z |
| format | Article |
| id | doaj.art-3b78184908d54e30996d442c4dab3a3b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T03:59:46Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-3b78184908d54e30996d442c4dab3a3b2023-11-23T10:46:12ZengMDPI AGSymmetry2073-89942021-12-011312236910.3390/sym13122369A Note on the Summation of the Incomplete Gamma FunctionRobert Reynolds0Allan Stauffer1Department of Mathematics and Statistics, York University, Toronto, ON M3J1P3, CanadaDepartment of Mathematics and Statistics, York University, Toronto, ON M3J1P3, CanadaWe examine the improved infinite sum of the incomplete gamma function for large values of the parameters involved. We also evaluate the infinite sum and equivalent Hurwitz-Lerch zeta function at special values and produce a table of results for easy reading. Almost all Hurwitz-Lerch zeta functions have an asymmetrical zero distribution.https://www.mdpi.com/2073-8994/13/12/2369Hurwitz-Lerch zeta functionincomplete gamma functionCatalan’s constantApréy’s constantCauchy integralcontour integral |
| spellingShingle | Robert Reynolds Allan Stauffer A Note on the Summation of the Incomplete Gamma Function Symmetry Hurwitz-Lerch zeta function incomplete gamma function Catalan’s constant Apréy’s constant Cauchy integral contour integral |
| title | A Note on the Summation of the Incomplete Gamma Function |
| title_full | A Note on the Summation of the Incomplete Gamma Function |
| title_fullStr | A Note on the Summation of the Incomplete Gamma Function |
| title_full_unstemmed | A Note on the Summation of the Incomplete Gamma Function |
| title_short | A Note on the Summation of the Incomplete Gamma Function |
| title_sort | note on the summation of the incomplete gamma function |
| topic | Hurwitz-Lerch zeta function incomplete gamma function Catalan’s constant Apréy’s constant Cauchy integral contour integral |
| url | https://www.mdpi.com/2073-8994/13/12/2369 |
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