East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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A NOTE ON THREE DERIVATIONS OF GREGORY-LEIBNIZ SERIES FOR π VIA A HYPERGEOMETRIC SERIES APPROACH

  • Dongkyu Lim (Department of Mathematics Education, Andong National University) ;
  • Arjun K. Rathie (Department of Mathematics, Vedant College of Engineering & Technology, (Rajasthan Technical University))
  • Received : 2022.12.11
  • Accepted : 2023.01.30
  • Published : 2023.05.31
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Abstract

The aim of this note is to provide three derivations of the well-known Gregory-Leibniz series for π via a hypergeometric series approach.

Keywords

Acknowledgement

The work of D. Lim was partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) NRF-2021R1C1C1010902.

References

  1. G. E. Andrews, R. Askey, and R. Roy, Special Functions, Cambridge University Press, Cambridge, 2000.
  2. W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935; Reprinted by Stechert-Hafner, New York, 1964.
  3. A. P. Prudrukov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 3; More special functions, Gordon Breach Science Publishers, Amsterdam, 1990.
  4. E. D. Rainville, Special Functions, The Macmillan Company, New York. 1960; Reprinted by chelsea Publishing Company, Bronx, NY, 1971.
  5. A. K. Rathie, and R. B. Paris, A note on applications of the Gregory-Leibniz series for π and its generalization, The Mathematics Student 91 (2022), no. 3-4, 43-53.
  6. L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, 1966.