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Notes

A Note on Beukers’s and Related Double Integrals

Pages 361-363 | Received 09 Mar 2018, Accepted 06 Oct 2018, Published online: 22 Apr 2019

References

  • Beukers, F. (1979). A note on the irrationality of ζ(2) and ζ(3). Bull. London Math. Soc. 11(3): 268–272. DOI: 10.1112/blms/11.3.268.
  • Chapman, R. (2004). A proof of Hadjicostas’ conjecture. arxiv.org/abs/math/0405478
  • Guillera, J., Sondow, J. (2006). Double integrals and infinite products for some classical constants via analytic continuations of Lerch’s transcendant. Ramanujan J. 16(3): 247–270. DOI: 10.1007/s11139-007-9102-0.
  • Hadjicostas, P. (2002). Some generalizations of Beukers’ integrals. Kyungpook Math. J. 42(2): 399–416.
  • Hadjicostas, P. (2004). A conjecture–generalization of Sondow’s formula. arxiv.org/abs/math/0405423
  • Lewin, L. (1981). Polylogarithms and Associated Functions. New York: North-Holland Publishers.
  • Sondow, J. (2003). Criteria for the irrationality of Euler’s constant. Proc. Amer. Math. Soc.131(11): 3335–3344. DOI: 10.1090/S0002-9939-03-07081-3.
  • Sondow, J. (2005). Double integrals for Euler’s constant and ln (4/π). Amer. Math. Monthly. 112(1): 61–65. DOI: 10.1080/00029890.2005.11920168.

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