A231132 Decimal expansion of sum_(n=2..infinity) (-1)^n*zeta(n)/n^2.

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

Offset: 0

Author

Jean-François Alcover, Nov 04 2013

Keywords

• nonn
• cons

Comments

Let f(k) = sum_(n=2..infinity) (-1)^n*zeta(n)/n^k, then Euler gamma is f(1) and this constant is f(2).

Examples

			0.32034114251279383627256109321177871875321147987620323852089693133571334868...
		

Links

• Eric Weisstein's MathWorld, Euler-Mascheroni Constant

Crossrefs

Cf. A001620, A352619, A355921, A365959.

Programs

Mathematica

RealDigits[ EulerGamma + Integrate[ LogGamma[x+1]/x, {x, 0, 1}] // N[#, 100]&, 10, 100] // First

PARI

sumalt(k=2,(-1)^k*zeta(k)/k^2) \\ Vaclav Kotesovec, Sep 23 2023