RAMANUJAN-SOLDNER CONSTANT

In mathematics, the 'Ramanujan-Soldner constant' is a mathematical constant defined as the unique positive zero of the logarithmic integral function.
Its value is approximately ''μ'' ≈ 1.451369234883381050283968485892027449493...
Since the logarithmic integral is defined by
: mathrm{li}(x) = int_0^x rac{dt}{ln t},
we have
: mathrm{li}(x);=;mathrm{li}(x) - mathrm{li}(mu)
: int_0^x rac{dt}{ln t} = int_0^x rac{dt}{ln t} - int_0^{mu} rac{dt}{ln t}
: mathrm{li}(x) = int_{mu}^x rac{dt}{ln t},
thus easing calculation for positive integers. Also, since the exponential integral function satisfies the equation
: mathrm{li}(x);=;mathrm{Ei}(ln{x}) ,
the only positive zero of the exponential integral occurs at the natural logarithm of the Ramanujan-Soldner constant, whose value is approximately ln(''μ'') ≈ 0.372507410781366634461991866...

Contents
See also
External links

See also



★ Logarithmic integral function

★ Exponential integral

External links



★

This article provided by Wikipedia. To edit the contents of this article, click here for original source.

psst.. try this: add to faves
©2009 TripAtlas.com