In mathematics, the Landau-Ramanujan constant occurs in a number theory result that the proportion of positive integers less than x which are the sum of two square numbers is, for large x, roughly proportional to
- <math>x/{\sqrt{\ln(x)}}.</math>
The constant of proportionality is the Landau-Ramanujan constant, which was discovered independently by Edmund Landau and Srinivasa Ramanujan. More formally, if N(x) is the number of positive integers less than x which are the sum of two squares, then
- <math>\lim_{x\rightarrow\infty} \frac{N(x)\sqrt{\ln(x)}}{x}\approx 0.76422365358922066299069873125.</math>
External links
- Eric W. Weisstein, Landau-Ramanujan Constant at MathWorld.
- Sloane's A064533 . The On-Line Encyclopedia of Integer Sequences (external link). AT&T Labs Research.
