Abstract
Recently, degenerate Bernstein polynomials have been introduced by Kim and Kim. In this paper, we investigate some properties and identities for the degenerate Bernstein polynomials associated with special numbers and polynomials including degenerate Bernstein polynomials and central factorial numbers of the second kind.
Highlights
Bernstein polynomials were first used by Bernstein in a constructive proof for the Stone– Weierstrass approximation theorem
The Bernstein polynomials are the mathematical basis for Bézier curves, which are frequently used in the mathematical field of numerical analysis
The study of degenerate versions of special numbers and polynomials began with the papers by Carlitz
Summary
Bernstein polynomials were first used by Bernstein in a constructive proof for the Stone– Weierstrass approximation theorem (see [2, 6, 21]). We will study for the degenerate Bernstein polynomials some fundamental properties and identities associated with special numbers and polynomials including degenerate Bernoulli polynomials and central factorial numbers of the second kind. Kim and Kim [12, 14] introduced the degenerate Bernstein polynomials of degree n, Bk,n(x|λ) (n, k ≥ 0), which are given by (x)k,λ tk(1 The degenerate Bernstein polynomials have been introduced recently by Kim and Kim. In this paper, we investigate some properties and identities for the degenerate Bernstein polynomials associated with special numbers and polynomials including degenerate Bernstein polynomials and central factorial numbers of the second kind.
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