Confluent hypergeometric function

Summary

A confluent hypergeometric function is a solution of Kummer's equation $z w'' + (b - z) w' - a w = 0$. The main one is Kummer's function $M(a, b, z) = {}_1F_1(a; b; z)$, the generalized hypergeometric series with one upper and one lower parameter. It is an entire function of $z$. Its special cases include the exponential function, the Laguerre polynomials, the error function and the incomplete gamma function.