# hypergeometric equation

The hypergeometric equation is the following linear ordinary differential equation:

 $x(1-x)y^{\prime\prime}+(c-(a+b+1)x)y^{\prime}-aby=0$

(Here, $a$, $b$, and $c$ are complex constants.)

The solutions of this equation may be expressed in terms of the hypergeometric function, hence the name.

The hypergeometric equation is a Fuchsian differential equation with singularities at $0$, $1$, and $\infty$. By a suitable change of variables, any second order Fuchsian differential equation may be converted into a hypergeometric equation.

Title hypergeometric equation HypergeometricEquation 2013-03-22 14:45:53 2013-03-22 14:45:53 rspuzio (6075) rspuzio (6075) 6 rspuzio (6075) Definition msc 33C05