On Degenerate Truncated Special Polynomials

Ugur Duran and Mehmet Acikgoz
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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

Mathematics, 2020, vol. 8, issue 1, 1-43

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.

Keywords: degenerate exponential function; truncated exponential function; special polynomials; special numbers; exponential generating function; bell polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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