A232734 Decimal expansion of Integral {x=0..infinity} 1/2^(2^x) dx.
5, 4, 6, 3, 0, 6, 8, 3, 5, 9, 5, 2, 4, 8, 2, 7, 4, 1, 7, 3, 6, 0, 9, 8, 7, 6, 9, 6, 2, 4, 1, 0, 1, 3, 8, 8, 9, 3, 7, 6, 3, 5, 5, 3, 9, 0, 8, 1, 6, 5, 9, 1, 3, 5, 4, 1, 6, 7, 8, 3, 3, 9, 9, 1, 7, 6, 1, 6, 3, 6, 8, 9, 8, 4, 1, 1, 9, 6, 5, 7, 6, 7, 6, 1, 7, 4, 1, 2, 2, 1, 6, 3, 4, 1, 0, 3, 9, 5, 4, 6
Offset: 0
Examples
0.546306835952482741736098769624101388937635539081659135416783399176163689841...
Links
- I. S. Gradsteyn, I. M. Ryzhik, Table of integrals, series and products, (1980) 8.212.
Programs
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Mathematica
RealDigits[-ExpIntegralEi[-Log[2]]/Log[2], 10, 100] // First
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PARI
eint1(log(2))/log(2) \\ Charles R Greathouse IV, Dec 02 2013
Formula
-Ei(-log(2))/log(2), where Ei is the exponential integral function.
Also equals (2*Integral_{x = 0..1/2} log(log(1/x)) dx - log(log(2)))/(2*log(2)).
From Peter Bala, Feb 05 2024: (Start)
Equals 1/log(2) * Integral_{x >= 1} 1/(x * 2^x) dx.
Equals 1/log(4) * Integral_{x = 0..1} 1/(log(2) - log(x)) dx.
Equals Integral_{x >= 1} log(x)/2^x dx = (log(2))^2 * Integral_{x >= 0} x*(2^x) /(2^(2^x)). See Gradsteyn and Ryzhik, Section 8.212, formulas (4) and (16). (End)