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A256919
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Decimal expansion of Sum_{k>=1} (zeta(4*k) - 1).
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13
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0, 8, 6, 6, 6, 2, 9, 7, 6, 2, 6, 5, 7, 0, 9, 4, 1, 2, 9, 3, 2, 9, 7, 4, 6, 0, 2, 6, 2, 4, 9, 9, 9, 7, 5, 4, 7, 7, 7, 1, 7, 1, 8, 6, 6, 7, 9, 8, 0, 9, 1, 6, 6, 7, 2, 1, 2, 4, 6, 8, 7, 5, 7, 8, 0, 4, 9, 2, 2, 8, 7, 6, 0, 4, 0, 8, 4, 4, 9, 8, 9, 1, 2, 8, 2, 1, 7, 2, 2, 4, 1, 2, 0, 3, 0, 2, 2, 5, 4, 0, 6, 1, 7, 4, 1
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OFFSET
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0,2
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REFERENCES
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H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights (2011) p. 265.
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LINKS
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Table of n, a(n) for n=0..104.
V. S. Adamchik, H. M. Srivastava, Some series of Zeta and related functions, Analysis (Munich) 18 (2) (1998) 131-144, eq. (2.25).
Eric Weisstein's MathWorld, Riemann Zeta Function
Wikipedia, Riemann Zeta Function
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FORMULA
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Equals 7/8 - (Pi/4)*coth(Pi).
Equals Sum_{n>=2} 1/(n^4 - 1). - Vaclav Kotesovec, Dec 08 2020
Equals (1/2)* Sum_{n>=2} 1/(n^2-1) - (1/2)* Sum_{n>=2} 1/(n^2+1) = (3/4 - A100554)/2. - R. J. Mathar, Jan 22 2021
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EXAMPLE
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0.0866629762657094129329746026249997547771718667980916672...
= -3 + Pi^4/90 + Pi^8/9450 + 691*Pi^12/638512875 + ...
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MATHEMATICA
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Join[{0}, RealDigits[7/8 - (Pi/4)*Coth[Pi], 10, 104] // First]
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CROSSREFS
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Cf. A013662, A013666, A013670, A175316, A256920, A339529, A339530, A339604 (3k-1).
Sequence in context: A003675 A254290 A121948 * A114141 A089139 A093209
Adjacent sequences: A256916 A256917 A256918 * A256920 A256921 A256922
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KEYWORD
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nonn,cons,easy
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AUTHOR
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Jean-François Alcover, Apr 13 2015
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STATUS
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approved
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