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A moment mu_n of a probability function P(x) taken about 0, mu_n^' = <x^n> (1) = intx^nP(x)dx. (2) The raw moments mu_n^' (sometimes also called "crude moments") can be ...

A number n such that sigma^2(n)=sigma(sigma(n))=2n, where sigma(n) is the divisor function is called a superperfect number. Even superperfect numbers are just 2^(p-1), where ...

Gram-Schmidt orthogonalization, also called the Gram-Schmidt process, is a procedure which takes a nonorthogonal set of linearly independent functions and constructs an ...

The inverse secant sec^(-1)z (Zwillinger 1995, p. 465), also denoted arcsecz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 315; Jeffrey 2000, p. 124), is ...

The Laplacian for a scalar function phi is a scalar differential operator defined by (1) where the h_i are the scale factors of the coordinate system (Weinberg 1972, p. 109; ...

The spherical harmonics can be generalized to vector spherical harmonics by looking for a scalar function psi and a constant vector c such that M = del x(cpsi) (1) = psi(del ...

A branch of mathematics that is a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given function has a ...

A differential evolution method used to minimize functions of real variables. Evolution strategies are significantly faster at numerical optimization than traditional genetic ...

Let R(z) be a rational function R(z)=(P(z))/(Q(z)), (1) where z in C^*, C^* is the Riemann sphere C union {infty}, and P and Q are polynomials without common divisors. The ...

Legendre-Gauss quadrature is a numerical integration method also called "the" Gaussian quadrature or Legendre quadrature. A Gaussian quadrature over the interval [-1,1] with ...