A352619 Decimal expansion of Sum_{k>=1} (-1)^(k+1) * zeta(2k+1)/(2k+1).

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

Offset: 0

Author

Bernard Schott, Mar 24 2022

Keywords

• nonn
• cons

Comments

Is there a closed-form formula for this constant as for A352527?

Examples

			0.2755753444339996627189...
		

References

• Bernard Candelpergher, Ramanujan Summation of Divergent Series, Springer, 2017, p. 35.

Links

• Cornel Ioan Vălean, Problema 327, La Gaceta de la Real Sociedad Matemática Española, Vol. 21, No. 2 (2018), pp. 331-343.

Crossrefs

Cf. A001620, A212880, A352527.

Programs

Maple

evalf(gamma + argument(I!),100);

Mathematica

RealDigits[EulerGamma + Arg[Gamma[1 + I]], 10, 100][[1]] (* Amiram Eldar, Mar 24 2022 *)

PARI

Euler + arg(I*gamma(I)) \\ Michel Marcus, Mar 25 2022

Formula

Equals gamma + arg(i!) (see Vălean).

Equals A001620 - A212880.

Equals Sum_{k>=1} (1/k - arctan(1/k)). - Amiram Eldar, Jul 21 2022