A Complete Asymptotic Expansion for Bernstein–Chlodovsky Polynomials for Functions on $$\mathbb {R}$$R

We consider a variant of the Bernstein–Chlodovsky polynomials approximating continuous functions on the entire real line and study its rate of convergence. The main result is a complete asymptotic expansion. As a special case we obtain a Voronovskaja-type formula previously derived by Karsli [11].