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NOTES ON SOME IDENTITIES INVOLVING THE RIEMANN ZETA FUNCTION
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 Title & Authors
NOTES ON SOME IDENTITIES INVOLVING THE RIEMANN ZETA FUNCTION
Lee, Hye-Rim; Ok, Bo-Myoung; Choi, June-Sang;
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 Abstract
We first review Ramaswami's find Apostol's identities involving the Zeta function in a rather detailed manner. We then present corrected, or generalized formulas, or a different method of proof for some of them. We also give closed-form evaluation of some series involving the Riemann Zeta function by an integral representation of ζ(s) and Apostol's identities given here.
 Keywords
Bernoulli numbers and polynomials;Riemann and Hurwitz Zeta functions;Harmonic numbers;Pochhammer symbol;Mobius function;
 Language
English
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 References
1.
Proc. Amer. Math. Soc., 1954. vol.5. pp.239-243 crossref(new window)

2.
Introduction to Analytic Number Theory, 1976.

3.
J. Math. Anal. Appl., 1999. vol.231. pp.91-117 crossref(new window)

4.
J. Comput. Appl. Math., 2000. vol.118. pp.87-109 crossref(new window)

5.
Higher Transcendental Functions, 1953. vol.I.

6.
J. London Math. Soc., 1934. vol.9. pp.165-169 crossref(new window)

7.
Riv. Mat. Univ. Parma, 1988. vol.14. 4, pp.1-23

8.
Kluwer Academic Publishers, 2001.

9.
A Course of Modern Analysis, Fourth Ed., 1963.