Degenerate Bernstein Polynomials

2018/06/17 by Taekyun Kim, Kim, Taekyun, Dae san Kim +1
Mathematics · #11B68 #11B83 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B68 #msc:11B83

paper · pdf · doi:10.48550/arxiv.1806.06379

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arxiv created 2018/06/17 · arxiv updated 2018/06/19

Abstract

Here we consider the degenerate Bernstein polynomials as a degenerate version of Bernstein polynomials, which are motivated by Simsek's recent work 'Generating functions for unification of the multidimensional Bernstein polynomials and their applications'([15,16]) and Carlitz's degenerate Bernoulli polynomials. We derived thier generating function, symmetric identities, recurrence relations, and some connections with generalized falling factorial polynomials, higher-order degenerate Bernoulli polynomials and degenerate Stirling numbers of the second kind.

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