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On Degenerate Truncated Special Polynomials

Author

Listed:
  • Ugur Duran

    (Department of the Basic Concepts of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Technical University, Hatay TR-31200, Turkey)

  • Mehmet Acikgoz

    (Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep TR-27310, Turkey)

Abstract

The main aim of this paper is to introduce the degenerate truncated forms of multifarious special polynomials and numbers and is to investigate their various properties and relationships by using the series manipulation method and diverse special proof techniques. The degenerate truncated exponential polynomials are first considered and their several properties are given. Then the degenerate truncated Stirling polynomials of the second kind are defined and their elementary properties and relations are proved. Also, the degenerate truncated forms of the bivariate Fubini and Bell polynomials and numbers are introduced and various relations and formulas for these polynomials and numbers, which cover several summation formulas, addition identities, recurrence relationships, derivative property and correlations with the degenerate truncated Stirling polynomials of the second kind, are acquired. Thereafter, the truncated degenerate Bernoulli and Euler polynomials are considered and multifarious correlations and formulas including summation formulas, derivation rules and correlations with the degenerate truncated Stirling numbers of the second are derived. In addition, regarding applications, by introducing the degenerate truncated forms of the classical Bernstein polynomials, we obtain diverse correlations and formulas. Some interesting surface plots of these polynomials in the special cases are provided.

Suggested Citation

  • Ugur Duran & Mehmet Acikgoz, 2020. "On Degenerate Truncated Special Polynomials," Mathematics, MDPI, vol. 8(1), pages 1-43, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:144-:d:311086
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    References listed on IDEAS

    as
    1. Ugur Duran & Mehmet Acikgoz, 2019. "Truncated Fubini Polynomials," Mathematics, MDPI, vol. 7(5), pages 1-15, May.
    2. Dan-Dan Su & Yuan He, 2019. "Some Identities for the Two Variable Fubini Polynomials," Mathematics, MDPI, vol. 7(2), pages 1-11, January.
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    Cited by:

    1. Ghulam Muhiuddin & Waseem Ahmad Khan & Ugur Duran, 2021. "Two-Variable Type 2 Poly-Fubini Polynomials," Mathematics, MDPI, vol. 9(3), pages 1-13, January.

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