A350763 Decimal expansion of gamma + log(2), where gamma is Euler's constant (A001620).

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

Offset

1,2

References

J. C. Kluyver, De constante van Euler en de natuurlijke getallen, Amst. Ak. Versl., Vol. 33 (1924), pp. 149-151.

Links

Table of n, a(n) for n=1..105.

Philippe Flajolet and Ilan Vardi, Zeta function expansions of classical constants, 1996.

Xavier Gourdon and Pascal Sebah, Collection of formulae for Euler's constant gamma, 2008.

Wikipedia, Harmonic numbers for real and complex values.

Formula

Equals A001620 + A002162.

Equals 1 + Sum_{k>=2} ((-1)^k * (zeta(k)-1)/k).

Equals 3/2 - Sum_{k>=2} ((-1)^k * (k-1) * (zeta(k)-1)/k) (Flajolet and Vardi, 1996).

Equals 5/4 - (1/2) * Sum_{k>=3} ((-1)^k * (k-1) * (zeta(k)-1)/k) (Gourdon and Sebah, 2008).

Equals 1 + Sum_{k>=2} (1/k - log(1+1/k)).

Equals 1 + Sum_{k>=0} abs(A002206(k))/((k+1)*(k+2)*A002207(k)) (Kluyver, 1924).

Equal Integral_{x>=0} (1/(1+x^2/4) - cos(x))/x dx = Integral_{x>=0} (1/(1+x^2) - cos(2*x))/x dx.

Equals Integral_{x=1..2} H(x) dx, where H(x) is the harmonic number for real variable x.

Example

1.27036284546147817002374421154057899911765947030017...

Mathematica

RealDigits[EulerGamma + Log[2], 10, 100][[1]]

Crossrefs

Cf. A001620, A002162, A002206, A002207.

Sequence in context: A188737 A200680 A260129 * A341318 A332324 A101689

Adjacent sequences: A350760 A350761 A350762 * A350764 A350765 A350766

Keyword

nonn,cons

Author

Amiram Eldar, Jan 14 2022

Status

approved