Lucky numbers share some properties with primes, such as asymptotic behaviour according to the prime number theorem; also, a version of Goldbach's conjecture has been extended to them.
12.
Regarding this asymptotic formula Mertens refers in his paper to " two curious formula of Legendre ", Note that, already in 1737, Euler knew the asymptotic behaviour of this sum.
13.
For " X " in \ mathfrak { a } _ +, the asymptotic behaviour of ? ? can be read off from this integral, leading to the formula:
14.
The field is indeed the " in " field we were seeking, as it describes the asymptotic behaviour of the interacting field as, though this statement will be made more precise later.
15.
It follows from the asymptotic behaviour of the Airy functions that both Ai ( " x " ) and Bi ( " x " ) have an infinity of zeros on the negative real axis.
16.
The first major general statement of the principle involved is that the asymptotic behaviour of " I " ( " k " ) depends only on the critical points of " f ".
17.
:: For small r ( prior to the first bifurcation ) the long term behaviour of a system governed by the logistic map is to tend towards a specific value x _ inf ( the asymptotic behaviour of the system ).
18.
We may expect the " in " field to resemble the asymptotic behaviour of the free field as, making the assumption that in the far away past interaction described by the current is negligible, as particles are far from each other.
19.
In the theory of probability, the "'Glivenko Cantelli theorem "', named after Valery Ivanovich Glivenko and Francesco Paolo Cantelli, determines the asymptotic behaviour of the empirical distribution function as the number of independent and identically distributed observations grows.
20.
The term is slowly gaining a broader usage in several fields of mathematics, including combinatorics and probability theory, whenever the quantitative features of a structure ( such as asymptotic behaviour ) can be deduced from a few global parameters appearing in the definition, without requiring knowledge of the details of the system.
