Szász–Mirakyan operator

In functional analysis, a discipline within mathematics, the Szász–Mirakyan operators (also spelled "Mirakjan" and "Mirakian") are generalizations of Bernstein polynomials to infinite intervals, introduced by Otto Szász in 1950 and G. M. Mirakjan in 1941. They are defined by

${\displaystyle \left[{\mathcal {S}}_{n}(f)\right](x):=e^{-nx}\sum _{k=0}^{\infty }{{\frac {(nx)^{k}}{k!}}f\left({\tfrac {k}{n}}\right)}}$

where ${\displaystyle x\in [0,\infty )\subset \mathbb {R} }$ and ${\displaystyle n\in \mathbb {N} }$.