Tricomi confluent hypergeometric function

Summary

The Tricomi confluent hypergeometric function $U(a, b, z)$ is the solution of Kummer's equation that behaves like $z^{-a}$ as $z \to +\infty$. It is a combination of two Kummer functions $M$. It grows or decays only like a power of $z$ at infinity, while $M(a, b, z)$ in general grows like $e^z$. Many functions of applied mathematics are special cases of $U$. Examples are the complementary error function, the upper incomplete gamma function and the modified Bessel function $K_\nu$.