Poisson-Charlier Function

$$\rho_n(\nu,x)\equiv {(1+\nu-n)_n\over \sqrt{n! x^n}} \,{}_1F_1(-n;1+\nu-n;x),$$

where $(a)_n$ is a Pochhammer Symbol and ${}_1F_1(a;b;z)$ is a Confluent Hypergeometric Function.

See also Poisson-Charlier Polynomial