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In mathematics, the Gaussian or ordinary hypergeometric function < sub > 2 </ sub > F < sub > 1 </ sub >( 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.