Gaussian differential equation

z(1 - z)(d^2 y)/(d z^2) + [c - (a + b + 1) z](d y)/(d z) - a b y = 0. It has regular singular points at 0, 1, and ∞. Every second-order ordinary differential equation with at most three regular singular points can be transformed into the hypergeometric differential equation.

confluent hypergeometric differential equation | confluent hypergeometric function of the first kind | generalized hypergeometric function | hypergeometric function