Simplify the confluent hypergeometric function with parameters $(n,1,z)$ Could you please provide a simple **closed form** expression for the confluent hyper-geometric function including the following (simple) parameters? ${}_1F_1(n,1,z)$ where n is positive integer and z is positive real. Thank you for time and patience.

I suppose this is related to my answer here. Though I think it would be more useful for you do a minimum of work yourself (by e.g. going to this Wiki page), I feel certain responsibility. So here it is: for integer $n\geq0$

$$ _1F_1(n+1,1,z)=\frac{z^{-n}}{n!}\left(z\circ\frac{d}{dz}\circ z\right)^ne^z.$$