Ramanujan-Soldner constant
Encyclopedia
In mathematics
, the Ramanujan–Soldner constant (also called the Soldner constant) is a mathematical constant
defined as the unique positive zero of the logarithmic integral function
. It is named after Srinivasa Ramanujan
and Johann Georg von Soldner
.
Its value is approximately μ ≈ 1.451369234883381050283968485892027449493…
Since the logarithmic integral is defined by
we have
thus easing calculation for positive integers. Also, since the exponential integral
function satisfies the equation
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…
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the Ramanujan–Soldner constant (also called the Soldner constant) is a mathematical constant
Mathematical constant
A mathematical constant is a special number, usually a real number, that is "significantly interesting in some way". Constants arise in many different areas of mathematics, with constants such as and occurring in such diverse contexts as geometry, number theory and calculus.What it means for a...
defined as the unique positive zero of the logarithmic integral function
Logarithmic integral function
In mathematics, the logarithmic integral function or integral logarithm li is a special function. It occurs in problems of physics and has number theoretic significance, occurring in the prime number theorem as an estimate of the number of prime numbers less than a given value.-Integral...
. It is named after Srinivasa Ramanujan
Srinivasa Ramanujan
Srīnivāsa Aiyangār Rāmānujan FRS, better known as Srinivasa Iyengar Ramanujan was a Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions...
and Johann Georg von Soldner
Johann Georg von Soldner
Johann Georg von Soldner was a German physicist, mathematician and astronomer, first in Berlin and later in 1808 in Munich.-Life:...
.
Its value is approximately μ ≈ 1.451369234883381050283968485892027449493…
Since the logarithmic integral is defined by
we have
thus easing calculation for positive integers. Also, since the exponential integral
Exponential integral
In mathematics, the exponential integral is a special function defined on the complex plane given the symbol Ei.-Definitions:For real, nonzero values of x, the exponential integral Ei can be defined as...
function satisfies the equation
the only positive zero of the exponential integral occurs at the natural logarithm
Natural logarithm
The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828...
of the Ramanujan–Soldner constant, whose value is approximately ln(μ) ≈ 0.372507410781366634461991866…