A248472 - OEIS

%I #32 Jun 13 2021 05:02:11

%S 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 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 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 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 G. C. Greubel, <a href="/A248472/b248472.txt">Table of n, a(n) for n = 0..10000</a>

%H Steven R. Finch, <a href="/A202501/a202501.pdf">Tauberian Constants</a>, August 30, 2004 [Cached copy, with permission of the author]

%H 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 Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>

%F C_1 also equals gamma + log(log(2)) + 2*Gamma(0, log(2)), where Gamma is the incomplete gamma function.

%e 0.96804483044204448704848730112285492269036397005924632964...

%p evalf(gamma + log(log(2)) - 2*Ei(-log(2)), 120); # _Vaclav Kotesovec_, Oct 27 2014

%t C1 = EulerGamma + Log[Log[2]] - 2*ExpIntegralEi[-Log[2]]; RealDigits[C1, 10, 103] // First

%o (PARI) Euler + log(log(2)) + 2*eint1(log(2)) \\ _Altug Alkan_, Sep 05 2018

%Y Cf. A001620, A074785, A249385.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Oct 27 2014