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].

中文翻译：

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$$ \ mathbb {R} $$ R上函数的Bernstein–Chlodovsky多项式的完全渐近展开

我们考虑了Bernstein-Chlodovsky多项式的一个变体，它逼近了整个实线上的连续函数，并研究了其收敛速度。主要结果是一个完整的渐近展开。作为一种特殊情况，我们获得了以前由Karsli推导的Voronovskaja型公式[11]。