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A248472 Decimal expansion of C_1 = gamma + log(log(2)) - 2*Ei(-log(2)), one of the Tauberian constants, where Ei is the exponential integral function.

%I A248472 #33 Feb 16 2025 08:33:23
%S A248472 9,6,8,0,4,4,8,3,0,4,4,2,0,4,4,4,8,7,0,4,8,4,8,7,3,0,1,1,2,2,8,5,4,9,
%T A248472 2,2,6,9,0,3,6,3,9,7,0,0,5,9,2,4,6,3,2,9,6,4,0,9,3,1,4,0,4,6,8,3,4,1,
%U A248472 5,6,2,4,9,1,1,6,6,1,3,1,4,3,5,9,1,5,1,2,0,1,8,1,6,6,4,2,9,5,8,9,2,4,2
%N A248472 Decimal expansion of C_1 = gamma + log(log(2)) - 2*Ei(-log(2)), one of the Tauberian constants, where Ei is the exponential integral function.
%H A248472 G. C. Greubel, <a href="/A248472/b248472.txt">Table of n, a(n) for n = 0..10000</a>
%H A248472 Steven R. Finch, <a href="/A202501/a202501.pdf">Tauberian Constants</a>, August 30, 2004 [Cached copy, with permission of the author]
%H A248472 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 68.
%H A248472 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>
%F A248472 C_1 also equals gamma + log(log(2)) + 2*Gamma(0, log(2)), where Gamma is the incomplete gamma function.
%e A248472 0.96804483044204448704848730112285492269036397005924632964...
%p A248472 evalf(gamma + log(log(2)) - 2*Ei(-log(2)), 120); # _Vaclav Kotesovec_, Oct 27 2014
%t A248472 C1 = EulerGamma + Log[Log[2]] - 2*ExpIntegralEi[-Log[2]]; RealDigits[C1, 10, 103] // First
%o A248472 (PARI) Euler + log(log(2)) + 2*eint1(log(2)) \\ _Altug Alkan_, Sep 05 2018
%Y A248472 Cf. A001620, A074785, A249385.
%K A248472 nonn,cons
%O A248472 0,1
%A A248472 _Jean-François Alcover_, Oct 27 2014