A256920 Decimal expansion of Sum_{k>=1} (-1)^k*(zeta(4k)-1) (negated).

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

Offset: 0

Author

Jean-François Alcover, Apr 13 2015

Keywords

• nonn
• cons
• easy

Examples

			-0.07847757966713683831802219324571923504667221732729...
= 1 - Pi^4/90 + Pi^8/9450 - 691*Pi^12/638512875 + ...
		

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
• Wikipedia, Riemann Zeta Function

Crossrefs

Cf. A013662, A013666, A013670, A256919.

Programs

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]

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