Kummer's equation

Summary

Kummer's equation is the second order linear differential equation $z w'' + (b - z) w' - a w = 0$, with complex parameters $a$ and $b$. It has a regular singular point at $0$ and an irregular singularity at $\infty$. Its solutions are the confluent hypergeometric functions, which include Laguerre polynomials, Hermite functions, the error function and the incomplete gamma function.