The logarithmic integral is defined as the
Cauchy principal value
Soldner's constant, denoted logarithmic
integral ,
(3)
so that
(4)
for A070769 ;
Derbyshire 2004, p. 114).
See also Exponential Integral ,
Logarithmic Integral ,
Riemann
Prime Counting Function ,
Soldner's
Constant Continued Fraction ,
Soldner's
Constant Digits
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References Berndt, B. C. Ramanujan's Notebooks, Part IV. Berndt,
B. C. and Evans, R. J. "Some Elegant Approximations and Asymptotic
Formulas for Ramanujan." J. Comput. Appl. Math. 37 , 35-41, 1991. Derbyshire,
J. Prime
Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Finch, S. R. "Euler-Gompertz Constant."
§6.2 in Mathematical
Constants. Hardy, G. H. Ramanujan:
Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. Le Lionnais, F. Les
nombres remarquables. Michon,
G. P. "Final Answers: Numerical Constants." http://home.att.net/~numericana/answer/constants.htm#mertens . Nielsen,
N. "Theorie des Integrallograrithmus und Verwandter Transzendenten." Part
II in Die
Gammafunktion. Ramanujan, S. Collected
Papers of Srinivasa Ramanujan Sloane,
N. J. A. Sequence A070769 in "The
On-Line Encyclopedia of Integer Sequences." Soldner. Abhandlungen 2 ,
333, 1812. Referenced on Wolfram|Alpha Soldner's Constant
Cite this as:
Weisstein, Eric W. "Soldner's Constant."
From MathWorld https://mathworld.wolfram.com/SoldnersConstant.html
Subject classifications
![lim_(epsilon->0^+)[int_0^(1-epsilon)(dt)/(lnt)+int_(1+epsilon)^x(dt)/(lnt)].](/images/equations/SoldnersConstant/Inline6.svg)
(or sometimes 
) is the root of the logarithmic
integral,
(Soldner 1812; Nielsen 1965, p. 88). Ramanujan calculated 
(Hardy 1999, Le Lionnais 1983, Berndt 1994),
while the correct value is 1.45136923488... (OEIS A070769;
Derbyshire 2004, p. 114).
