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Goh-Schmutz Constant

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The Goh-Schmutz constant is defined by the integrals

C=int_0^infty(ln(1+t))/(e^t-1)dt
(1)
=int_0^inftyln[1-ln(1-e^(-t))]dt
(2)
=int_0^infty(te^(-t))/((1-e^(-t))[1-ln(1-e^(-t))])dt
(3)

and the sum

C=-sum_(k=1)^infty(e^k)/kEi(-k),
(4)

where Ei(x) is the exponential integral. It has numerical value

C=1.1178641511899...
(5)

(OEIS A143300).

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References

Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, p. 287, 2003.Sloane, N. J. A. Sequence A143300 in "The On-Line Encyclopedia of Integer Sequences."

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Goh-Schmutz Constant

Cite this as:

Weisstein, Eric W. "Goh-Schmutz Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Goh-SchmutzConstant.html

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