On Degenerate Truncated Special Polynomials
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 exponentia...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/1/144 |
| _version_ | 1819077528628756480 |
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| author | Ugur Duran Mehmet Acikgoz |
| author_facet | Ugur Duran Mehmet Acikgoz |
| author_sort | Ugur Duran |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-21T18:58:38Z |
| format | Article |
| id | doaj.art-95a295396aa746abb2ab7acba8b77692 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-21T18:58:38Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-95a295396aa746abb2ab7acba8b776922022-12-21T18:53:33ZengMDPI AGMathematics2227-73902020-01-018114410.3390/math8010144math8010144On Degenerate Truncated Special PolynomialsUgur Duran0Mehmet Acikgoz1Department of the Basic Concepts of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Technical University, Hatay TR-31200, TurkeyDepartment of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep TR-27310, TurkeyThe 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.https://www.mdpi.com/2227-7390/8/1/144degenerate exponential functiontruncated exponential functionspecial polynomialsspecial numbersexponential generating functionbell polynomials |
| spellingShingle | Ugur Duran Mehmet Acikgoz On Degenerate Truncated Special Polynomials Mathematics degenerate exponential function truncated exponential function special polynomials special numbers exponential generating function bell polynomials |
| title | On Degenerate Truncated Special Polynomials |
| title_full | On Degenerate Truncated Special Polynomials |
| title_fullStr | On Degenerate Truncated Special Polynomials |
| title_full_unstemmed | On Degenerate Truncated Special Polynomials |
| title_short | On Degenerate Truncated Special Polynomials |
| title_sort | on degenerate truncated special polynomials |
| topic | degenerate exponential function truncated exponential function special polynomials special numbers exponential generating function bell polynomials |
| url | https://www.mdpi.com/2227-7390/8/1/144 |
| work_keys_str_mv | AT ugurduran ondegeneratetruncatedspecialpolynomials AT mehmetacikgoz ondegeneratetruncatedspecialpolynomials |