In mathematics, the symmetric derivative is an operation generalizing the ordinary derivative. It is defined as: lim h → 0 f ( x + h ) − f ( x − h ) 2 h . {\displaystyle \lim...

In mathematics, an iterated function is a function X → X (that is, a function from some set X to itself) which is obtained by composing another function f : X → X with itself a certain number of times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial number, the result of applying a given function is fed again in the function as input, and this process is repeated. Iterated functions are objects of study in computer science, fractals, dynamical systems, mathematics and renormalization group physics. == Definition == The formal...

In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. The theorem was proved independently by Jacques Hadamard and Charles Jean de la Vallée-Poussin in 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function). The first such distribution found is π(N) ~ N/log(N), where π(N) is the prime-counting function and log(N) is the natural logarithm...