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 $\mathrm{\infty }$. By a suitable change of variables, any second order Fuchsian differential equation may be converted into a hypergeometric equation.

Title	hypergeometric equation
Canonical name	HypergeometricEquation
Date of creation	2013-03-22 14:45:53
Last modified on	2013-03-22 14:45:53
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	6
Author	rspuzio (6075)
Entry type	Definition
Classification	msc 33C05