Hypergeometric function 2F1(a,b,c,x) is defined as

Hypergeometric function is a solution of hypergeometric differential equation

Hypergeometric function is a generalization of a series of elementary and special functions. Bessel functions, incomplete gamma function, elliptic integrals and orthogonal polynomials are particular cases of hypergeometric function. Many elementary functions could be written by using the hypergeometric function, for example:

Hypergeometric2F1 subroutine calculates hypergeometric function for real x in (-1,1).