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.
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, 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, 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
Offset: 0
Examples
0.96804483044204448704848730112285492269036397005924632964...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..10000
- Steven R. Finch, Tauberian Constants, August 30, 2004 [Cached copy, with permission of the author]
- Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 68.
- Eric Weisstein's MathWorld, Exponential Integral
Programs
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Maple
evalf(gamma + log(log(2)) - 2*Ei(-log(2)), 120); # Vaclav Kotesovec, Oct 27 2014
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Mathematica
C1 = EulerGamma + Log[Log[2]] - 2*ExpIntegralEi[-Log[2]]; RealDigits[C1, 10, 103] // First
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PARI
Euler + log(log(2)) + 2*eint1(log(2)) \\ Altug Alkan, Sep 05 2018
Formula
C_1 also equals gamma + log(log(2)) + 2*Gamma(0, log(2)), where Gamma is the incomplete gamma function.