| ファイル情報(添付) | |
| タイトル |
INTEGRALS WITH POWERS OF THE ARCTAN FUNCTION VIA EULER SUMS
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| 著者 |
SOFO ANTHONY
NIMBRAN AMRIK SINGH
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| 収録物名 |
島根大学総合理工学部紀要.シリーズB
Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics
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| 巻 | 56 |
| 開始ページ | 1 |
| 終了ページ | 17 |
| 収録物識別子 |
ISSN 1342-7121
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| 内容記述 |
その他
We undertake an investigation into families of integrals containing powers of the inverse tangent and log functions. It will be shown that Euler sums play an important part in the evaluation of these integrals. In a special case of the parameters, our analysis generalizes an arctan integral studied by Ramanujan [11]. In another special case, we prove that the corresponding log tangent integral can be represented as a linear combination of the product of zeta functions and the Dirichlet beta function. We also deduce formulas for log-sine and log-cosine integrals.
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| 言語 |
英語
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| 資源タイプ | 紀要論文 |
| 出版者 |
総合理工学部
The Interdisciplinary Graduate School of Science and Engineering
|
| 発行日 | 2023 |
| 出版タイプ | Version of Record（出版社版。早期公開を含む） |
| アクセス権 | オープンアクセス |
| 関連情報 |
ソウゴウ リコウ ガクブ
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