## Soldner's Constant

Consider the following formulation of the Prime Number Theorem,

where is the Möbius Function and (sometimes also denoted ) is Soldner's constant. Ramanujan found (Hardy 1969, Le Lionnais 1983, Berndt 1994). Soldner (cited in Nielsen 1965) derived the correct value of as 1.4513692346..., where is the root of

(Le Lionnais 1983).

References

Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, pp. 123-124, 1994.

Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, p. 45, 1959.

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 39, 1983.

Nielsen, N. Théorie des Integrallogarithms. New York: Chelsea, p. 88, 1965.