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Euler Sums and Integral Connections

Author

Listed:
  • Anthony Sofo

    (College of Engineering and Science, Victoria University, P. O. Box 14428, Melbourne City, Victoria 8001, Australia)

  • Amrik Singh Nimbran

    (B3-304, Palm Grove Heights, Ardee City, Gurugram, Haryana 122003, India)

Abstract

In this paper, we present some Euler-like sums involving partial sums of the harmonic and odd harmonic series. First, we give a brief historical account of Euler’s work on the subject followed by notations used in the body of the paper. After discussing some alternating Euler sums, we investigate the connection of integrals of inverse trigonometric and hyperbolic type functions to generate many new Euler sum identities. We also give some new identities for Catalan’s constant, Apery’s constant and a fast converging identity for the famous ζ ( 2 ) constant.

Suggested Citation

  • Anthony Sofo & Amrik Singh Nimbran, 2019. "Euler Sums and Integral Connections," Mathematics, MDPI, vol. 7(9), pages 1-24, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:833-:d:265649
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    Citations

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    Cited by:

    1. Kwang-Wu Chen, 2024. "On General Alternating Tornheim-Type Double Series," Mathematics, MDPI, vol. 12(17), pages 1-30, August.
    2. Chunli Li & Wenchang Chu, 2024. "Evaluating Infinite Series Involving Harmonic Numbers by Integration," Mathematics, MDPI, vol. 12(4), pages 1-21, February.
    3. Kwang-Wu Chen, 2024. "On Some General Tornheim-Type Series," Mathematics, MDPI, vol. 12(12), pages 1-18, June.
    4. Chunli Li & Wenchang Chu, 2022. "Improper Integrals Involving Powers of Inverse Trigonometric and Hyperbolic Functions," Mathematics, MDPI, vol. 10(16), pages 1-19, August.

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