A380547 Decimal expansion of the absolute value of the sum of the Dirichlet L-series A000035 at s=1/2.

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

Offset: 0

Author

R. J. Mathar, Jan 26 2025

Keywords

• nonn
• cons

Comments

Defined as L(s) = (1-2^(-s))*zeta(s) by analytic continuation of the Riemann zeta function.

Examples

			Sum_{n>=1} A000035(n)/sqrt(n) = -0.42772793269397822132111661913967125635373339294116...
		

Crossrefs

Cf. A111003 (s=2), A233091 (s=3), A300707 (s=4), A059750 (zeta(1/2)), A000035, A010503, A113024, A268682.

Programs

Mathematica

RealDigits[(1/Sqrt[2]-1)*Zeta[1/2], 10, 120][[1]] (* Amiram Eldar, Jan 26 2025 *)

PARI

(1/sqrt(2)-1)*zeta(1/2) \\ Amiram Eldar, Jan 26 2025

Formula

Equals A268682*A059750.

Equals A010503 * A113024 = Sum_{n>=1} (-1)^(n+1)/sqrt(2*n). - Amiram Eldar, Jan 26 2025