A386518 Decimal expansion of (log(2*Pi)-1)/2 + gamma.

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

Offset: 0

Author

R. J. Mathar, Jul 24 2025

Keywords

• cons
• nonn

Comments

This is [x^2]G(x), the quadratic coefficient of the Taylor expansion of Barnes' G-function around zero. G(x) = x + this*x^2 -1.114914..*x^3 +O(x^4).

Examples

			0.9961541981062056023868418264880200709035568095777...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• R. J. Mathar, Erratum to Exercise A4.2 in "An introduction to the theory of the Riemann Zeta Function", viXra:2507.0094 (2025), coefficient h_2.
• Wikipedia, Barnes G-function

Crossrefs

Cf. A122914, A001620.

Programs

Maple

log(2*Pi)/2-1/2+gamma ; evalf(%) ;

Mathematica

First[RealDigits[(Log[2*Pi] - 1)/2 + EulerGamma, 10, 100]] (* Paolo Xausa, Jul 24 2025 *)

Formula

Equals A122914 -1 + A001620.