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Notes

A Proof of ζ(2)=π2/6 Involving a Fourier–Legendre Expansion

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Pages 349-352 | Received 11 Mar 2023, Accepted 08 Aug 2023, Published online: 05 Jan 2024

References

  • Borwein, J. M., Borwein, P. B. (1987). Pi and the AGM. A Study in Analytic Number Theory and Computational Complexity. New York: Wiley.
  • Choe, B. R. (1987). An elementary proof of ∑n=1∞1/n2=π2/6. Amer. Math. Monthly. 94(7): 662–663.
  • Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G., eds. (1953). Higher Transcendental Functions, Vols. I, II. New York-Toronto-London: McGraw-Hill Book Co., Inc.
  • González, M. O. (1954). Elliptic integrals in terms of Legendre polynomials. Proc. Glasg. Math. Assoc. 2: 97–99. DOI: 10.1017/S2040618500033104.
  • Knopp, K. (1928). Theory and Application of Infinite Series. London: Blackie & Son.
  • Rainville, E. D. (1960). Special Functions. New York: The Macmillan Company.
  • Slater, L. J. (1966). Generalized Hypergeometric Functions. Cambridge: Cambridge Univ. Press.

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