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Improper Integrals Involving Powers of Inverse Trigonometric and Hyperbolic Functions

Author

Listed:
  • 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
    Department of Mathematics and Physics, University of Salento, 73100 Lecce, Italy)

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.

Suggested Citation

  • Chunli Li & Wenchang Chu, 2022. "Improper Integrals Involving Powers of Inverse Trigonometric and Hyperbolic Functions," Mathematics, MDPI, vol. 10(16), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2980-:d:891784
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    References listed on IDEAS

    as
    1. Anthony Sofo & Amrik Singh Nimbran, 2019. "Euler Sums and Integral Connections," Mathematics, MDPI, vol. 7(9), pages 1-24, September.
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    Cited by:

    1. Hari Mohan Srivastava, 2022. "Higher Transcendental Functions and Their Multi-Disciplinary Applications," Mathematics, MDPI, vol. 10(24), pages 1-3, December.

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