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Degenerate Bernstein polynomials

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

A Correction to this article was published on 11 March 2019

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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’ (Simsek in Filomat 30(7):1683–1689, 2016, Math Methods Appl Sci 1–12, 2018) and Carlitz’s degenerate Bernoulli polynomials. We derived their 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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Change history

  • 11 March 2019

    Unfortunately, erratua appear in the statement corresponding Theorems 2.6 and 2.10 in the original paper .

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Acknowledgements

We would like to thank the referee for his valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Kwangwoon University, Seoul, 139-701, Republic of Korea

    Taekyun Kim

  2. Department of Mathematics, Sogang University, Seoul, 121-742, Republic of Korea

    Dae San Kim

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  1. Taekyun Kim
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  2. Dae San Kim
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Correspondence to Taekyun Kim.

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Kim, T., Kim, D.S. Degenerate Bernstein polynomials. RACSAM 113, 2913–2920 (2019). https://doi.org/10.1007/s13398-018-0594-9

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  • DOI: https://doi.org/10.1007/s13398-018-0594-9

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