# Hypergeometric Function

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).

### Other articles related to "hypergeometric function, functions, function, hypergeometric functions":

Hypergeometric Function - Values At Special Points z - Other Points
... There are many other formulas giving the hypergeometric function as an algebraic number at special rational values of the parameters, some of which are listed in (Gessel ...
Hypergeometric Differential Equation - Special Cases
... Many of the common mathematical functions can be expressed in terms of the hypergeometric function, or as limiting cases of it ... Some typical examples are The confluent hypergeometric function (or Kummer's function) can be given as a limit of the hypergeometric function so all functions that are essentially special ... These include most of the commonly used functions of mathematical physics ...
Meijer G-function - Relationship Between The G-function and The Generalized Hypergeometric Function
... m, then the Meijer G-function can be expressed as a sum of residues in terms of generalized hypergeometric functions pFq−1 (Slater's theorem) For the integral to ... Γ(0) with 1, and in the argument of the hypergeometric function, if we recall the meaning of the vector notation, this amounts to shortening the vector length from q to q−1 ... n, then the G-function can be expressed as For this, either p > q, or p = q and

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