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A New Generating Function of ( ) Bernstein-Type Polynomials and Their Interpolation Function

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  • Yilmaz Simsek
  • Mehmet Acikgoz

Abstract

The main object of this paper is to construct a new generating function of the ( ) Bernstein-type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and derivative of the ( ) Bernstein-type polynomials. We also give relations between the ( ) Bernstein-type polynomials, Hermite polynomials, Bernoulli polynomials of higher order, and the second-kind Stirling numbers. By applying Mellin transformation to this generating function, we define interpolation of the ( ) Bernstein-type polynomials. Moreover, we give some applications and questions on approximations of ( ) Bernstein-type polynomials, moments of some distributions in Statistics.

Suggested Citation

  • Yilmaz Simsek & Mehmet Acikgoz, 2010. "A New Generating Function of ( ) Bernstein-Type Polynomials and Their Interpolation Function," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-12, March.
    • Handle: RePEc:hin:jnlaaa:769095
    DOI: 10.1155/2010/769095
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    Cited by:

    1. Kucukoglu, Irem & Simsek, Buket & Simsek, Yilmaz, 2019. "Multidimensional Bernstein polynomials and Bezier curves: Analysis of machine learning algorithm for facial expression recognition based on curvature," Applied Mathematics and Computation, Elsevier, vol. 344, pages 150-162.
    2. Dmitry Kruchinin & Vladimir Kruchinin & Yuriy Shablya, 2021. "Method for Obtaining Coefficients of Powers of Bivariate Generating Functions," Mathematics, MDPI, vol. 9(4), pages 1-17, February.
    3. Dmitry V. Kruchinin & Yuriy V. Shablya, 2015. "Explicit Formulas for Meixner Polynomials," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-5, October.

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