Improper Integrals Involving Powers of Inverse Trigonometric and Hyperbolic Functions

Chunli Li and Wenchang Chu ()
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Chunli Li: School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
Wenchang Chu: School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China

Mathematics, 2022, vol. 10, issue 16, 1-19

Abstract: Three classes of improper integrals involving higher powers of arctanh , arctan, and arcsin are examined using the recursive approach. Numerous explicit formulae are established, which evaluate these integrals in terms of π , ln 2 , the Riemann zeta function, and the Dirichlet beta function.

Keywords: integration by parts; trigonometric functions; Fourier series; Riemann zeta function; Dirichlet beta function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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