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A256920 Decimal expansion of Sum_{k>=1} (-1)^k*(zeta(4k)-1) (negated). 3
0, 7, 8, 4, 7, 7, 5, 7, 9, 6, 6, 7, 1, 3, 6, 8, 3, 8, 3, 1, 8, 0, 2, 2, 1, 9, 3, 2, 4, 5, 7, 1, 9, 2, 3, 5, 0, 4, 6, 6, 7, 2, 2, 1, 7, 3, 2, 7, 2, 9, 1, 3, 2, 7, 5, 8, 7, 4, 8, 6, 6, 4, 5, 7, 9, 3, 8, 0, 8, 4, 4, 8, 0, 6, 1, 6, 8, 1, 1, 1, 7, 4, 5, 7, 3, 1, 9, 4, 3, 5, 4, 1, 6, 6, 6, 2, 8, 6, 3, 8, 3, 1, 6, 6, 7, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights (2011) p. 265.
LINKS
V. S. Adamchi, H. M. Srivastava, Some series of the zeta and related functions, Analysis (Munich) 18 (1998) 271-288, eq (2.26)
Eric Weisstein's MathWorld, Riemann Zeta Function
FORMULA
1 + (Pi/(2*Sqrt(2)))*(sin(Pi*sqrt(2)) + sinh(Pi*sqrt(2))) / (cos(Pi*sqrt(2)) - cosh(Pi*sqrt(2))).
Equals Sum_{k>=2} 1/(k^4 + 1). - Amiram Eldar, Jul 11 2020
EXAMPLE
-0.07847757966713683831802219324571923504667221732729...
= 1 - Pi^4/90 + Pi^8/9450 - 691*Pi^12/638512875 + ...
MATHEMATICA
Join[{0}, RealDigits[1 + (Pi/(2 Sqrt[2]))*(Sin[Pi*Sqrt[2]] + Sinh[Pi*Sqrt[2]]) / (Cos[Pi*Sqrt[2]] - Cosh[Pi*Sqrt[2]]), 10, 105] // First]
CROSSREFS
Sequence in context: A194642 A114857 A292823 * A307065 A344965 A195340
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)