Riemann's differential equation

Summary

Riemann's differential equation is the general second-order linear Fuchsian equation with exactly three regular singular points on the Riemann sphere. It is determined by the positions of the three points and the two exponents at each. The six exponents must add up to $1$. The hypergeometric differential equation is the case where the points are $0$, $1$ and $\infty$. Every Riemann equation reduces to it by a Möbius transformation and a power factor.