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A method for numerical solution of a second-order ordinary differential equation y^('')=f(x,y) first expounded by Gauss. It proceeds by introducing a function delta^(-2)f ...

Jacobi-Gauss quadrature, also called Jacobi quadrature or Mehler quadrature, is a Gaussian quadrature over the interval [-1,1] with weighting function ...

The operator of fractional integration is defined as _aD_t^(-nu)f(t)=1/(Gamma(nu))int_a^tf(u)(t-u)^(nu-1)du for nu>0 with _aD_t^0f(t)=f(t) (Oldham and Spanier 1974, Miller ...

A singular integral is an integral whose integrand reaches an infinite value at one or more points in the domain of integration. Even so, such integrals can converge, in ...

X is a spherical t-design in E iff it is possible to exactly determine the average value on E of any polynomial f of degree at most t by sampling f at the points of X. In ...

The divisor function sigma_k(n) for n an integer is defined as the sum of the kth powers of the (positive integer) divisors of n, sigma_k(n)=sum_(d|n)d^k. (1) It is ...

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. More ...

A recursively enumerable set A is creative if its complement is productive. Creative sets are not recursive. The property of creativeness coincides with completeness. Namely, ...

pi has decimal expansion given by pi=3.141592653589793238462643383279502884197... (1) (OEIS A000796). The following table summarizes some record computations of the digits of ...

A univariate function f(x) is said to be even provided that f(x)=f(-x). Geometrically, such functions are symmetric about the y-axis. Examples of even functions include 1 ...