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Four Classes of Definite Integrals about Hyperbolic and Trigonometric Functions
- Authors: Li C.1, Chu W.1,2
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Affiliations:
- School of Mathematics and Statistics, Zhoukou Normal University
- Department of Mathematics and Physics, University of Salento
- Issue: Vol 63, No 7 (2023)
- Pages: 1108
- Section: Ordinary differential equations
- URL: https://journals.rcsi.science/0044-4669/article/view/136180
- DOI: https://doi.org/10.31857/S0044466923070086
- EDN: https://elibrary.ru/ZXSPUW
- ID: 136180
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Abstract
By establishing recurrence relations and then determining boundary values, we examine four classes of definite integrals of xm over higher powers of cosh x, sinh x, cos x and sin x in denominators. They are explicitly evaluated in terms of the logarithm function, the Riemann zeta function and its variants, such as Dirichlet beta function and Legendre’s chi-function.
About the authors
C. Li
School of Mathematics and Statistics, Zhoukou Normal University
Email: lichunlizk@outlook.com
Henan, China
W. Chu
School of Mathematics and Statistics, Zhoukou Normal University; Department of Mathematics and Physics, University of Salento
Author for correspondence.
Email: chu.wenchang@unisalento.it
Henan, China; 73100, Lecce, Italy
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