A371803 Decimal expansion of Sum_{k>=0} (-1)^k / (k^2 + 4).

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

Offset: 0

Author

Clark Kimberling, Apr 17 2024

Keywords

• nonn
• cons

Examples

			0.1279333824131754728739815724485566356111330...
		

Crossrefs

Cf. A329085.

Programs

Mathematica

s = Re[N[Sum[(-1)^k/(k^2 + 4), {k, 0, Infinity}], 120]]
First[RealDigits[s]]

Formula

Equals (1/8)*(1 + 2*Pi*csch(2*Pi)).

Equals 1/8 + Pi*exp(2*Pi)/(2*(exp(4*Pi) - 1)). - Vaclav Kotesovec, Apr 22 2024