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A350763
Decimal expansion of gamma + log(2), where gamma is Euler's constant (A001620).
1
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
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.
Alessandro Languasco and Pieter Moree, Euler constants from primes in arithmetic progression, arXiv:2406.16547 [math.NT], 2024. See p. 18, Table 1.
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.
Equals 2*A228725. - Hugo Pfoertner, Jul 03 2024
EXAMPLE
1.2703628454614781700237442115405789991176594703...
MATHEMATICA
RealDigits[EulerGamma + Log[2], 10, 100][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jan 14 2022
STATUS
approved