A339083 Decimal expansion of Sum_{k>=0} (zeta(4*k+2)-1).

6, 6, 3, 3, 3, 7, 0, 2, 3, 7, 3, 4, 2, 9, 0, 5, 8, 7, 0, 6, 7, 0, 2, 5, 3, 9, 7, 3, 7, 5, 0, 0, 0, 2, 4, 5, 2, 2, 2, 8, 2, 8, 1, 3, 3, 2, 0, 1, 9, 0, 8, 3, 3, 2, 7, 8, 7, 5, 3, 1, 2, 4, 2, 1, 9, 5, 0, 7, 7, 1, 2, 3, 9, 5, 9, 1, 5, 5, 0, 1, 0, 8, 7, 1, 7, 8, 2, 7, 7, 5, 8, 7, 9, 6, 9, 7, 7, 4, 5, 9, 3, 8, 2, 5, 8, 9, 4, 5

Offset: 0

Author

Artur Jasinski, Dec 24 2020

Keywords

• nonn
• cons

Comments

Sum_{k>=1} zeta(4*k)-1 see A256919.

Sum_{k>=1} zeta(4*k+1)-1 see A339097.

Sum_{k>=0} zeta(4*k+3)-1 see A338858.

For additional comments and generalization see A339604.

Examples

			0.663337023734290587067025397375...
		

Crossrefs

Cf. A024006, A256919, A338815, A338858, A339097, A339135, A339529, A339530, A339604, A339605, A339605.

Programs

Mathematica

RealDigits[N[Sum[Zeta[4 n + 2] - 1, {n, 0, Infinity}], 105]][[1]]

PARI

suminf(k=0, zeta(4*k+2)-1) \\ Michel Marcus, Dec 24 2020

Formula

Equals Sum_{k>=2} k^2/(k^4-1).

Equals -1/8 + Pi*coth(Pi)/4 = -1/8 + A338815 = 3/4 - A256919.

Extensions

a(104) corrected and more terms from Georg Fischer, Jun 06 2024