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Evaluation of Infinite Series by Integrals

Author

Listed:
  • Chunli Li

    (School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China)

  • Wenchang Chu

    (Department of Mathematics and Physics, University of Salento, 73100 Lecce, Italy)

Abstract

We examine a large class of infinite triple series and establish a general summation formula. This is done by expressing the triple series in terms of definite integrals involving arctangent function that are evaluated in turn in closed forms. Numerous explicit formulae are tabulated for the triple series whose values result in elegant expressions as π , ln 2 and the Catalan constant G .

Suggested Citation

  • Chunli Li & Wenchang Chu, 2022. "Evaluation of Infinite Series by Integrals," Mathematics, MDPI, vol. 10(14), pages 1-14, July.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2444-:d:861931
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    References listed on IDEAS

    as
    1. Jocemar Q. Chagas & José A. Tenreiro Machado & António M. Lopes, 2022. "Revisiting the Formula for the Ramanujan Constant of a Series," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
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    Cited by:

    1. Mohammad Abu-Ghuwaleh & Rania Saadeh & Ahmad Qazza, 2022. "General Master Theorems of Integrals with Applications," Mathematics, MDPI, vol. 10(19), pages 1-19, September.

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    1. Mohammad Abu-Ghuwaleh & Rania Saadeh & Ahmad Qazza, 2022. "General Master Theorems of Integrals with Applications," Mathematics, MDPI, vol. 10(19), pages 1-19, September.

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