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A series for ζ(s)

Published online by Cambridge University Press:  20 January 2009

U. Balakrishnan
U. Balakrishnan
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India
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We obtain a series representation for ζ(s) valid in Res> – k(<0). This representation is obtained by a sequence of regrouping of the series 1–2−s + 3−s–4−s + …( = (1—21−s)ζ(s), Re s > 0). We can obtain asymptotic relations like

as an application of our series representation for ζ(s).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 2 , June 1988 , pp. 205 - 210
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCE

1.Berndt, Bruce C. and Ivans, Ronald J., Chapter 7 of Ramanujan's second Notebook, Proc. Indian Acad. Sci. Math. Sci. 92 (1983), 67–96.CrossRefGoogle Scholar