Integral and Series Representations of Riemann's Zeta Function and Dirichlet's Eta Function and a Medley of Related Results
Contour integral representations of Riemann's Zeta function and Dirichlet's Eta (alternating Zeta) function are presented and investigated. These representations flow naturally from methods developed in the 1800s, but somehow they do not appear in the standard reference summaries, textbook...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/181724 |
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| _version_ | 1832556588785729536 |
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| author | Michael S. Milgram |
| author_facet | Michael S. Milgram |
| author_sort | Michael S. Milgram |
| collection | DOAJ |
| description | Contour integral representations of Riemann's Zeta function and Dirichlet's Eta (alternating Zeta) function are presented and investigated. These representations flow naturally from methods developed in the 1800s, but somehow they do not appear in the standard reference summaries, textbooks, or literature. Using these representations as a basis, alternate derivations of known series and integral representations for the Zeta and Eta function are obtained on a unified basis that differs from the textbook approach, and results are developed that appear to be new. |
| format | Article |
| id | doaj-art-08021f556e0548f6b1b4117ad9b8a4fe |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-08021f556e0548f6b1b4117ad9b8a4fe2025-02-03T05:44:48ZengWileyJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/181724181724Integral and Series Representations of Riemann's Zeta Function and Dirichlet's Eta Function and a Medley of Related ResultsMichael S. Milgram0Consulting Physicist, Geometrics Unlimited, Ltd., P.O. Box 1484, Deep River, ON, K0J 1P0, CanadaContour integral representations of Riemann's Zeta function and Dirichlet's Eta (alternating Zeta) function are presented and investigated. These representations flow naturally from methods developed in the 1800s, but somehow they do not appear in the standard reference summaries, textbooks, or literature. Using these representations as a basis, alternate derivations of known series and integral representations for the Zeta and Eta function are obtained on a unified basis that differs from the textbook approach, and results are developed that appear to be new.http://dx.doi.org/10.1155/2013/181724 |
| spellingShingle | Michael S. Milgram Integral and Series Representations of Riemann's Zeta Function and Dirichlet's Eta Function and a Medley of Related Results Journal of Mathematics |
| title | Integral and Series Representations of Riemann's Zeta Function and Dirichlet's Eta Function and a Medley of Related Results |
| title_full | Integral and Series Representations of Riemann's Zeta Function and Dirichlet's Eta Function and a Medley of Related Results |
| title_fullStr | Integral and Series Representations of Riemann's Zeta Function and Dirichlet's Eta Function and a Medley of Related Results |
| title_full_unstemmed | Integral and Series Representations of Riemann's Zeta Function and Dirichlet's Eta Function and a Medley of Related Results |
| title_short | Integral and Series Representations of Riemann's Zeta Function and Dirichlet's Eta Function and a Medley of Related Results |
| title_sort | integral and series representations of riemann s zeta function and dirichlet s eta function and a medley of related results |
| url | http://dx.doi.org/10.1155/2013/181724 |
| work_keys_str_mv | AT michaelsmilgram integralandseriesrepresentationsofriemannszetafunctionanddirichletsetafunctionandamedleyofrelatedresults |