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Czasopismo

1999 | 90 | 1 | 79-89

Tytuł artykułu

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

Treść / Zawartość

Języki publikacji

EN

Czasopismo

Rocznik

Tom

90

Numer

1

Strony

79-89

Daty

wydano
1999
otrzymano
1998-10-05
poprawiono
1999-03-12

Twórcy

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

Bibliografia

  • [Ay] R. Ayoub, Euler and the zeta function, Amer. Math. Monthly 81 (1974), 1067-1086.
  • [Ch] B. R. Choe, An elementary proof of $∑_{n=1}^∞ 1/n² = π^{2}/6$, Amer. Math. Monthly 94 (1987), 662-663.
  • [CK] D. Cvijović and J. Klinowski, New rapidly convergent series representations for ζ(2n+1), Proc. Amer. Math. Soc. 125 (1997), 1263-1271.
  • [Ew1] J. A. Ewell, A new series representation for ζ(3), Amer. Math. Monthly 97 (1990), 219-220.
  • [Ew2] J. A. Ewell, On values of the Riemann zeta function at integral arguments, Canad. Math. Bull. 34 (1991), 60-66.
  • [Ew3] J. A. Ewell, On the zeta function values ζ(2k+1), k=1,2,..., Rocky Mountain J. Math. 23 (1995), 1003-1012.
  • [Iv] A. Ivić, The Riemann Zeta-Function, Wiley, New York, 1985.
  • [Ka1] M. Katsurada, Power series with the Riemann zeta-function in the coefficients, Proc. Japan Acad. Ser. A 72 (1996), 61-63.
  • [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.
  • [Ka3] M. Katsurada, Power series and asymptotic series associated with the Lerch zeta-function, Proc. Japan Acad. Ser. A 74 (1998), 167-170.
  • [Ra] V. Ramaswami, Notes on Riemann's ζ-function, J. London Math. Soc. 9 (1934), 165-169.
  • [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.
  • [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.
  • [Sr3] H. M. Srivastava, Some rapidly converging series for ζ(2n+1), Proc. Amer. Math. Soc. 127 (1999), 385-396.
  • [Ti] E. C. Titchmarsh, The Theory of the Riemann Zeta-function, 2nd ed., revised by D. R. Heath-Brown, Oxford Univ. Press, 1986.
  • [Wa] L. C. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982.
  • [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.
  • [YW] Z.-N. Yue and K. S. Williams, Some series representations of ζ(2n+1), Rocky Mountain J. Math. 23 (1993), 1581-1591.

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