Definite integral of the logarithm hyperbolic secant function in terms of the Hurwitz zeta function
We evaluate definite integrals of the form given by $\int_{0}^{\infty}R(a, x)\log (\cos (\alpha) \text{sech}(x)+1)dx$. The function $R(a, x)$ is a rational function with general complex number parameters. Definite integrals of this form yield closed forms for famous integrals in the books of Bierens...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-12-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021082?viewType=HTML |