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language
eng
Author
SOFO, ANTHONY
NIMBRAN, AMRIK SINGH
Description
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.
Journal Title
Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics
Volume
56
Start Page
1
End Page
17
ISSN
1342-7121
Published Date
2023
Publisher
総合理工学部
Publisher Aalternative
The Interdisciplinary Graduate School of Science and Engineering
NII Type
Departmental Bulletin Paper
Format
PDF
Text Version
出版社版
OAI-PMH Set
Faculty of Science and Engineering
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