Soldner,s Constant
المؤلف:
Berndt, B. C.
المصدر:
Ramanujan,s Notebooks, Part IV. New York: Springer-Verlag
الجزء والصفحة:
...
29-3-2020
1788
Soldner's Constant
The logarithmic integral is defined as the Cauchy principal value
Soldner's constant, denoted 
(or sometimes 
) is the root of the logarithmic integral,
 |
(3)
|
so that
 |
(4)
|
for 
(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).
REFERENCES:
Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, pp. 123-124, 1994.
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. New York: Penguin, 2004.
Finch, S. R. "Euler-Gompertz Constant." §6.2 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 423-428, 2003.
Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, pp. 23 and 45, 1999.
Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 39, 1983.
Michon, G. P. "Final Answers: Numerical Constants." https://home.att.net/~numericana/answer/constants.htm#mertens.
Nielsen, N. "Theorie des Integrallograrithmus und Verwandter Transzendenten." Part II in Die Gammafunktion. New York: Chelsea, 1965.
Ramanujan, S. Collected Papers of Srinivasa Ramanujan (Ed. G. H. Hardy, P. V. S. Aiyar, and B. M. Wilson). Providence, RI: Amer. Math. Soc., p. 351, 2000.
Sloane, N. J. A. Sequence A070769 in "The On-Line Encyclopedia of Integer Sequences."
Soldner. Abhandlungen 2, 333, 1812.
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