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ArticleOriginal scientific text

Title

Rapidly convergent series representations for ζ(2n+1) and their χ-analogue

Authors 1

Affiliations

  1. Department of Mathematics and Computer Science, Kagoshima University, 1-21-35, Korimoto, Kagoshima 890-0065, Japan

Keywords

ENG
Riemann zeta-function, Dirichlet L-function, Mellin-Barnes integral, series representation

Bibliography

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  3. [CK] D. Cvijović and J. Klinowski, New rapidly convergent series representations for ζ(2n+1), Proc. Amer. Math. Soc. 125 (1997), 1263-1271.
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  8. [Ka1] M. Katsurada, Power series with the Riemann zeta-function in the coefficients, Proc. Japan Acad. Ser. A 72 (1996), 61-63.
  9. [Ka2] M. Katsurada, On Mellin-Barnes type of integrals and sums associated with the Riemann zeta-function, Publ. Inst. Math. (Beograd) (N.S.) 62 (76) (1997), 13-25.
  10. [Ka3] M. Katsurada, Power series and asymptotic series associated with the Lerch zeta-function, Proc. Japan Acad. Ser. A 74 (1998), 167-170.
  11. [Ra] V. Ramaswami, Notes on Riemann's ζ-function, J. London Math. Soc. 9 (1934), 165-169.
  12. [Sr1] H. M. Srivastava, A unified presentation of certain classes of series of the Riemann zeta function, Riv. Mat. Univ. Parma (4) 14 (1988), 1-23.
  13. [Sr2] H. M. Srivastava, Certain families of rapidly convergent series representations for ζ(2n+1), Math. Sci. Research Hot-Line 1 (6) (1997), 1-6.
  14. [Sr3] H. M. Srivastava, Some rapidly converging series for ζ(2n+1), Proc. Amer. Math. Soc. 127 (1999), 385-396.
  15. [Ti] E. C. Titchmarsh, The Theory of the Riemann Zeta-function, 2nd ed., revised by D. R. Heath-Brown, Oxford Univ. Press, 1986.
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  17. [Wi] J. R. Wilton, A proof of Burnside's formula for Γ(x+1) and certain allied properties of Riemann's ζ-function, Messenger Math. 52 (1922/1923), 90-93.
  18. [YW] Z.-N. Yue and K. S. Williams, Some series representations of ζ(2n+1), Rocky Mountain J. Math. 23 (1993), 1581-1591.
Acta Arithmetica
1999/90/1
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Pages:
79-89
Main language of publication
English
Received
1998-10-05
Accepted
1999-03-12
Published
1999
Exact and natural sciences