On an Exact Relation between ζ″(2) and the Meijer
G
-Functions
Keyword(s):
In this paper we consider some integral representations for the evaluation of the coefficients of the Taylor series for the Riemann zeta function about a point in the complex half-plane ℜ ( s ) > 1 . Using the standard approach based upon the Euler-MacLaurin summation, we can write these coefficients as Γ ( n + 1 ) plus a relatively smaller contribution, ξ n . The dominant part yields the well-known Riemann’s zeta pole at s = 1 . We discuss some recurrence relations that can be proved from this standard approach in order to evaluate ζ ″ ( 2 ) in terms of the Euler and Glaisher-Kinkelin constants and the Meijer G -functions.
2002 ◽
Vol 142
(2)
◽
pp. 435-439
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Keyword(s):
Keyword(s):
2010 ◽
Vol 466
(2124)
◽
pp. 3679-3692
◽
Keyword(s):
Keyword(s):