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Triple Series Evaluated in π and \(\ln 2\) as Well as Catalan’s Constant G

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Abstract

By computing definite integrals, several infinite triple series are explicitly evaluated in terms of \(\pi \) and \(\ln 2\) as well as Catalan’s constant \(G\).

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REFERENCES

  1. N. Batir, “Finite binomial sum identities with harmonic numbers,” J. Integer Seq. 24, 21.4.3 (2021).

  2. K. N. Boyadzhiev, “Power series with skew-harmonic numbers, dilogarithms, and double integrals,” Tatra Mt. Mat. Publ. 56, 93–108 (2013).

    MathSciNet  Google Scholar 

  3. D. M. Bradley, “Representations of Catalan’s constant” (2001). www.researchgate.net/publication/2325473

  4. H. Chen, “Interesting series associated with central binomial coefficients, Catalan numbers and harmonic numbers,” J. Integer Seq. 19, 16.1.5 (2016).

  5. W. Chu, “A binomial coefficient identity associated with Beukers’ conjecture on Apéry numbers,” Electron. J. Combin. 11, 15 (2004).

    Article  Google Scholar 

  6. W. Chu, “Summation formulae involving harmonic numbers,” Filomat 26 (1), 143–152 (2012).

    Article  MathSciNet  Google Scholar 

  7. W. Chu and L. De Donno, “Hypergeometric series and harmonic number identities,” Adv. Appl. Math. 34, 123–137 (2005).

    Article  MathSciNet  Google Scholar 

  8. R. Frontczak, “Binomial sums with skew-harmonic numbers,” Palest. J. Math. 10, 756–763 (2021).

    MathSciNet  Google Scholar 

  9. G. Jameron and N. Lord, “Integrals evaluated in terms of Catalan’s constant,” Math. Gaz. 101, 38–49 (2017).

    Article  MathSciNet  Google Scholar 

  10. L. Kargin and M. Can, “Harmonic number identities via polynomials with r-Lah coefficients,” C. R. Math. Acad. Sci. Paris 358, 535–550 (2020).

    Article  MathSciNet  Google Scholar 

  11. C. L. Li and W. Chu, “Evaluation of infinite series by integrals,” Mathematics 10, 2444 (2022). https://doi.org/10.3390/math10142444

    Article  Google Scholar 

  12. A. Sofo, Computational Techniques for the Summation of Series (Kluwer Academic, New York, 2003).

    Book  Google Scholar 

  13. S. M. Stewart, “A Catalan constant inspired integral odyssey,” Math. Gaz. 104, 449–459 (2020).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhoukou Normal University, Henan, China

    Chunli Li & Wenchang Chu

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  1. Chunli Li
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  2. Wenchang Chu
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Correspondence to Chunli Li or Wenchang Chu.

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Li, C., Chu, W. Triple Series Evaluated in π and \(\ln 2\) as Well as Catalan’s Constant G. Comput. Math. and Math. Phys. 63, 2005–2023 (2023). https://doi.org/10.1134/S0965542523110143

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  • DOI: https://doi.org/10.1134/S0965542523110143

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