A256920 - OEIS

%I #13 Aug 06 2024 07:18:18

%S 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,

%T 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,

%U 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

%N Decimal expansion of Sum_{k>=1} (-1)^k*(zeta(4k)-1) (negated).

%D H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights (2011) p. 265.

%H V. S. Adamchi, H. M. Srivastava, <a href="https://citeseerx.ist.psu.edu/pdf/b75ac68b32e8225460584eb7c6c00bb6214b3f51">Some series of the zeta and related functions</a>, Analysis (Munich) 18 (1998) 271-288, eq (2.26)

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>

%F 1 + (Pi/(2*Sqrt(2)))*(sin(Pi*sqrt(2)) + sinh(Pi*sqrt(2))) / (cos(Pi*sqrt(2)) - cosh(Pi*sqrt(2))).

%F Equals Sum_{k>=2} 1/(k^4 + 1). - _Amiram Eldar_, Jul 11 2020

%e -0.07847757966713683831802219324571923504667221732729...

%e = 1 - Pi^4/90 + Pi^8/9450 - 691*Pi^12/638512875 + ...

%t 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]

%Y Cf. A013662, A013666, A013670, A256919.

%K nonn,cons,easy

%O 0,2

%A _Jean-François Alcover_, Apr 13 2015