A371802 Decimal expansion of Sum_{k>=0} (-1)^k / (k^2 + 3).

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

Offset: 0

Author

Clark Kimberling, Apr 17 2024

Keywords

• nonn
• cons

Comments

In general, for m > 0, Sum_{k>=0} (-1)^k / (k^2 + m) = 1/(2*m) + Pi * exp(sqrt(m)*Pi) / ((exp(2*sqrt(m)*Pi) - 1) * sqrt(m)). - Vaclav Kotesovec, Apr 22 2024

Examples

			0.17452676963383902546102623598943384481...
		

Crossrefs

Cf. A329084.

Programs

Mathematica

s = Re[N[Sum[(-1)^k/(k^2 + 3), {k, 0, Infinity}], 120]]
First[RealDigits[s]]

PARI

sumalt(k=0, (-1)^k / (k^2 + 3)) \\ Hugo Pfoertner, Apr 22 2024

Formula

Equals (1/6)*(1 + sqrt(3)*Pi*csch(Pi*sqrt(3))).