# Hypergeometric 1F1

The hypergeometric function ${}_1F_1$ (sometimes denoted by $M$, sometimes called the confluent hypergeometric function of the first kind) is defined by the series $${}_1F_1(a;b;z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(a)_k z^k}{(b)_k k!},$$ where $(a)_k$ denotes the Pochhammer symbol and $k!$ denotes the factorial.