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Volumn 97, Issue 1, 1998, Pages 1-15

Further series representations for ζ(2n + 1)

Author keywords

Asymptotic expansion; Bernoulli numbers and polynomials; Binomial theorem; Functional equation; Harmonic numbers; L'h pital's rule; Pochhammer symbol; Watson's lemma; Zeta functions

Indexed keywords


EID: 0012754313     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(97)10145-X     Document Type: Article
Times cited : (19)

References (12)
  • 1
    • 0003669011 scopus 로고
    • Oxford University Press/Clarendon Press, Oxford/London, 1951; 2nd ed., revised by D.R. Heath-Brown
    • E.C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford University Press/Clarendon Press, Oxford/London, 1951; 2nd ed., revised by D.R. Heath-Brown, 1986.
    • (1986) The Theory of the Riemann Zeta-Function
    • Titchmarsh, E.C.1
  • 2
    • 23644439770 scopus 로고    scopus 로고
    • Some rapidly converging series for ζ(2n + 1)
    • to be published
    • H.M. Srivastava, Some rapidly converging series for ζ(2n + 1), Proc. Amer. Math. Soc., to be published.
    • Proc. Amer. Math. Soc.
    • Srivastava, H.M.1
  • 3
    • 0001847762 scopus 로고
    • A proof of Burnside's formula for Γ(x + 1) and certain allied properties of Riemann's ζ-function
    • 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.
    • (1922) Messenger Math. , vol.52 , pp. 90-93
    • Wilton, J.R.1
  • 5
    • 21744449094 scopus 로고    scopus 로고
    • New rapidly convergent series representations for ζ(2n + 1)
    • D. Cvijović, J. Klinowski, New rapidly convergent series representations for ζ(2n + 1), Proc. Amer. Math. Soc. 125 (1997) 1263-1271.
    • (1997) Proc. Amer. Math. Soc. , vol.125 , pp. 1263-1271
    • Cvijović, D.1    Klinowski, J.2
  • 6
    • 84881570063 scopus 로고
    • Some series representations of ζ(2n + 1)
    • N.-Y. Zhang, K.S. Williams, Some series representations of ζ(2n + 1), Rocky Mountain J. Math. 23 (1993) 1581-1592.
    • (1993) Rocky Mountain J. Math. , vol.23 , pp. 1581-1592
    • Zhang, N.-Y.1    Williams, K.S.2
  • 7
    • 0000894249 scopus 로고
    • On evaluation of the Dirichlet series at positive integers by q-calculation
    • H. Tsumura, On evaluation of the Dirichlet series at positive integers by q-calculation, J. Number Theory 48 (1994) 383-391.
    • (1994) J. Number Theory , vol.48 , pp. 383-391
    • Tsumura, H.1
  • 8
    • 84881277236 scopus 로고
    • On the Zeta function values ζ(2k + 1), k = 1, 2, . .
    • J.A. Ewell, On the Zeta function values ζ(2k + 1), k = 1, 2, . . ., Rocky Mountain J. Math. 25 (1995) 1003-1012.
    • (1995) Rocky Mountain J. Math. , vol.25 , pp. 1003-1012
    • Ewell, J.A.1
  • 11
    • 38249026905 scopus 로고
    • Sums of certain series of the Riemann Zeta function
    • H.M. Srivastava, Sums of certain series of the Riemann Zeta function, J. Math. Anal. Appl. 134 (1988) 129-140.
    • (1988) J. Math. Anal. Appl. , vol.134 , pp. 129-140
    • Srivastava, H.M.1
  • 12
    • 84966208674 scopus 로고
    • An asymptotic expansion for the first derivative of the generalized Riemann Zeta function
    • E. Elizalde, An asymptotic expansion for the first derivative of the generalized Riemann Zeta function, Math. Comput. 47 (1986) 347-350.
    • (1986) Math. Comput. , vol.47 , pp. 347-350
    • Elizalde, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.