Hypergeometric Functions

Hypergeometric Functions

In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is a solution of a second-order linear ordinary differential equation (ODE). Every second-order linear ODE with three regular singular points can be transformed into this equation.

For systematic lists of some of the many thousands of published identities involving the hypergeometric function, see the reference works by Arthur Erdélyi, Wilhelm Magnus, and Fritz Oberhettinger et al. (1953), Abramowitz & Stegun (1965), and Daalhuis (2010).

Read more about Hypergeometric Functions:  History, The Hypergeometric Series, Special Cases, The Hypergeometric Differential Equation, Gauss' Contiguous Relations, Transformation Formulas, Values At Special Points z

Famous quotes containing the word functions:

    The mind is a finer body, and resumes its functions of feeding, digesting, absorbing, excluding, and generating, in a new and ethereal element. Here, in the brain, is all the process of alimentation repeated, in the acquiring, comparing, digesting, and assimilating of experience. Here again is the mystery of generation repeated.
    Ralph Waldo Emerson (1803–1882)