A345202 Decimal expansion of gamma + zeta(2), where gamma is Euler's constant (A001620).

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

Offset: 1

Author

Amiram Eldar, Jun 10 2021

Keywords

• nonn
• cons

Comments

The value of the sum (see the Formula section) discovered in 1926 by the Italian mathematician and historian of science Giovanni Enrico Eugenio Vacca (1872-1953).

Examples

			2.22214973174975929707892725672842762026110923714672...
		

References

• G. Vacca, Nuova serie per la costante di Eulero, C=0,577..., Rendiconti, Accademia Nazionale dei Lincei, Roma, Classe di Scienze Fisiche, Matematiche e Naturali, Serie 6, Vol. 3 (1926), pp. 19-20.

Links

• Ettore Carruccio, Giovanni Vacca, matematico, storico e filosofo della scienza, Bollettino dell'Unione Matematica Italiana, Serie 3, Vol. 8 (1953), pp. 448-456.
• Tanguy Rivoal, Is Euler's constant a value of an arithmetic special function?, 2017.

Crossrefs

Cf. A001620, A013661, A048760.

Programs

Mathematica

RealDigits[EulerGamma + Pi^2/6, 10, 100][[1]]

Formula

Equals Sum_{k>=1} (1/floor(sqrt(k))^2 - 1/k) (Vacca, 1926).

Equals Sum_{k>=1} f(k)/k^2, where f(k) = Sum_{j=1..2*k} j/(j + k^2).

Equals A001620 + A013661.