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 Explore with Wolfram|Alpha 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)].](https://mathworld.wolfram.com/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). 