Abstract
In the present paper, we give the explicit formula of the principal part of $$ \sum\limits_{k = 0}^n {([k]_q - [n]_q x)^s x^k } \prod\limits_{m = 0}^{n - k - 1} {(1 - q^m x)} $$ with respect to [n]q for any integer s and q ∈ (0,1]. And, using the expressions, we obtain saturation theorems for Bn(f,qn;x) approximating to f(x) ∈ C[0,1], 0 < qn ≤ 1, qn → 1.
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