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Values of the Riemann Zeta Function and the Dirichlet Beta Function at Positive Integer Points and Multiple Numerical Series

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References

  1. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover Publ., New York, 1972).

    MATH  Google Scholar 

  2. S. R. Finch, Mathematical Constants (Cambridge Univ. Press, Cambridge, 2003).

    MATH  Google Scholar 

  3. NIST Handbook of Mathematical Functions (Cambridge, New York, 2010).

  4. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Vol. 1. Elementary Functions (Gordon and Breach, Philadelphia, 1986).

    MATH  Google Scholar 

  5. L. Tornheim, Amer. J. Math. 72, 303 (1950).

    Article  MathSciNet  Google Scholar 

  6. L. J. Mordell, J. London Math. Soc. 33, 368 (1958).

    Article  MathSciNet  Google Scholar 

  7. I. A Aliev, Tornheim-Like Series, Harmonic Numbers and Zeta Values, arXiv: 2008.02488 (2020).

    MATH  Google Scholar 

  8. D. Leshchiner, J. Number Theory 13, 355 (1981).

    Article  MathSciNet  Google Scholar 

  9. K. A. Mirzoev and T. A. Safonova, Dokl. Math. 98 (2), 486 (2018).

    Article  MathSciNet  Google Scholar 

  10. K. A. Mirzoev and T. A. Safonova, Trans. Moscow Math. Soc. 80, 133 (2019).

    Article  MathSciNet  Google Scholar 

  11. K. A. Mirzoev and T. A. Safonova, Dokl. Ross. Akad. Nauk Matem., Inform., Prots. Upr. 494, 48 (2020).

    Google Scholar 

  12. B. C. Berndt, Ramanujann’s Notebooks. Part I (Springer, New York, 1985).

    Book  MATH  Google Scholar 

  13. D. M. Bradley, Representations of Catalan’s constant (2001), Unpublished Note.

    Google Scholar 

  14. R. C Boo, Amer. Math. Monthly 94 (7), 662 (1987).

    MathSciNet  Google Scholar 

  15. P. Flajolet and B. Salvy, Experiment. Math. 7 (1), 15 (1998).

    Article  MathSciNet  Google Scholar 

  16. J. M. Borwein, Amer. Math. Monthly 115 (2), 125 (2008).

    Article  MathSciNet  Google Scholar 

  17. J. M. Borwein and K. Dilcher, Ramanujan J. 45 (2), 413 (2018).

    Article  MathSciNet  Google Scholar 

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Funding

This work was supported by the Russian Science Foundation under grant 20-11-20261.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119992, Russia

    K. A. Mirzoev

  2. Moscow Center for Fundamental and Applied Mathematics, Moscow, 119899, Russia

    K. A. Mirzoev & T. A. Safonova

  3. Lomonosov Northern (Arctic) Federal University, Arkhangelsk, 163002, Russia

    T. A. Safonova

Authors
  1. K. A. Mirzoev
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  2. T. A. Safonova
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Corresponding author

Correspondence to K. A. Mirzoev.

Additional information

Translated from Matematicheskie Zametki, 2022, Vol. 112, pp. 947–952 https://doi.org/10.4213/mzm13534.

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Mirzoev, K.A., Safonova, T.A. Values of the Riemann Zeta Function and the Dirichlet Beta Function at Positive Integer Points and Multiple Numerical Series. Math Notes 112, 1071–1076 (2022). https://doi.org/10.1134/S0001434622110396

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  • DOI: https://doi.org/10.1134/S0001434622110396

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