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: ОБЫКНОВЕННЫЕ ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ
- URL: https://journals.rcsi.science/0044-4669/article/view/136180
- DOI: https://doi.org/10.31857/S0044466923070086
- EDN: https://elibrary.ru/ZXSPUW
- ID: 136180
Cite item
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