Search Results for ""

Discrete Mathematics

A generalized Fourier series is a series expansion of a function based on the special properties of a complete orthogonal system of functions. The prototypical example of ...

In his famous paper of 1859, Riemann stated that the number N(T) of Riemann zeta function zeros sigma+it with 0<t<=T is asymptotically given by ...

Consider the inequality sigma(n)<e^gammanlnlnn for integer n>1, where sigma(n) is the divisor function and gamma is the Euler-Mascheroni constant. This holds for 7, 11, 13, ...

Stirling's approximation gives an approximate value for the factorial function n! or the gamma function Gamma(n) for n>>1. The approximation can most simply be derived for n ...

The number one (1), also called "unity," is the first positive integer. It is an odd number. Although the number 1 used to be considered a prime number, it requires special ...

An even number is an integer of the form n=2k, where k is an integer. The even numbers are therefore ..., -4, -2, 0, 2, 4, 6, 8, 10, ... (OEIS A005843). Since the even ...

A field which is complete with respect to a discrete valuation is called a local field if its field of residue classes is finite. The Hasse principle is one of the chief ...

A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of a function f(x) is a point x_0 ...

Let T_n(x) be an arbitrary trigonometric polynomial T_n(x)=1/2a_0+{sum_(k=1)^n[a_kcos(kx)+b_ksin(kx)]} (1) with real coefficients, let f be a function that is integrable over ...