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

Acta Arithmetica

Volumn 90, Issue 1, 1999, Pages 79-89

  Katsurada, Masanori ^a,b  

^a KAGOSHIMA UNIVERSITY   (Japan)

^b KEIO UNIVERSITY   (Japan)

Author keywords

Dirichlet L function; Mellin Barnes integral; Riemann zeta function; Series representation

Indexed keywords

EID: 0001799697     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa-90-1-79-89     Document Type: Article

References (18)

1. R. Ayoub, Euler and the zeta function, Amer. Math. Monthly 81 (1974), 1067-1086.
2. 2/6, ibid. 94 (1987), 662-663.
3. D. Cvijović and J. Klinowski, New rapidly convergent series representations for ζ(2n + 1), Proc. Amer. Math. Soc. 125 (1997), 1263-1271.
4. J. A. Ewell, A new series representation for ζ(3), Amer. Math. Monthly 97 (1990), 219-220.
5. _, On values of the Riemann zeta function at integral arguments, Canad. Math. Bull. 34 (1991), 60-66.
6. _, On the zeta function values ζ(2k + 1), k = 1, 2, . . . , Rocky Mountain J. Math. 23 (1995), 1003-1012.
7. A. Ivić, The Riemann Zeta-Function, Wiley, New York, 1985.
8. M. Katsurada, Power series with the Riemann zeta-function in the coefficients, Proc. Japan Acad. Ser. A 72 (1996), 61-63.
9. 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. _, Power series and asymptotic series associated with the Lerch zeta-function, Proc. Japan Acad. Ser. A 74 (1998), 167-170.
11. V. Ramaswami, Notes on Riemann's ζ-function, J. London Math. Soc. 9 (1934), 165-169.
12. 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. _, Certain families of rapidly convergent series representations for ζ(2n + 1), Math. Sci. Research Hot-Line 1 (6) (1997), 1-6.
14. _, Some rapidly converging series for ζ(2n + 1), Proc. Amer. Math. Soc. 127 (1999), 385-396.
15. E. C. Titchmarsh, The Theory of the Riemann Zeta-function, 2nd ed., revised by D. R. Heath-Brown, Oxford Univ. Press, 1986.
16. L. C. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982.
17. J. R. Wilton, A proof of Burnside's formula for log Γ(x + 1) and certain allied properties of Riemann's ζ-function, Messenger Math. 52 (1922/1923), 90-93.
18. Z.-N. Yue and K. S. Williams, Some series representations of ζ(2n + 1), Rocky Mountain J. Math. 23 (1993), 1581-1591.