A372363 Decimal expansion of Sum_{k>=0} (-1)^k * k / (k^2+1).

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

Offset

0,1

Links

Table of n, a(n) for n=0..85.

Example

-0.26961050270800898180149496765207091895000208950017220...

Mathematica

s = Sum[(-1)^k k/(k^2 + 1), {k, 0, Infinity}]
d = Chop[N[s, 100]]
First[RealDigits[d]]
(* or *)
RealDigits[Chop[N[(PolyGamma[0, -I/2] + PolyGamma[0, I/2] - PolyGamma[0, 1/2 - I/2] - PolyGamma[0, 1/2 + I/2])/4, 200]], 10, 100][[1]] (* Vaclav Kotesovec, Oct 15 2025 *)

Crossrefs

Cf. A372364.

Sequence in context: A362533 A346406 A078437 * A235997 A360957 A155678

Adjacent sequences: A372360 A372361 A372362 * A372364 A372365 A372366

Keyword

nonn,cons

Author

Clark Kimberling, May 01 2024

Status

approved