 |  |  |
(1)
|
 |  | ![lim_(epsilon->0^+)[int_0^(1-epsilon)(dt)/(lnt)+int_(1+epsilon)^x(dt)/(lnt)].](/images/equations/SoldnersConstant/Inline6.svg) |
(2)
|
索爾德納常數，記為 
(或有時為 
) 是 對數積分 的根，
 |
(3)
|
因此
 |
(4)
|
對於 
(Soldner 1812; Nielsen 1965, p. 88)。 拉馬努金計算出 
(Hardy 1999, Le Lionnais 1983, Berndt 1994)，而正確值為 1.45136923488... (OEIS A070769; Derbyshire 2004, p. 114)。
索爾德納常數
另請參閱
指數積分, 對數積分, 黎曼素數計數函式, 索爾德納常數連分數, 索爾德納常數數字使用 探索
參考文獻
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." http://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.在 中被引用
索爾德納常數請引用為
Weisstein, Eric W. "Soldner's Constant." 來自 Web 資源。 https://mathworld.tw/SoldnersConstant.html