scholarly journals Unified Degenerate Central Bell Polynomials

2019 ◽  
Author(s):  
Mehmet Acikgoz ◽  
Ugur Duran
Keyword(s):  
Explicit Formula ◽  
Bernstein Polynomials ◽  
Summation Formula ◽  
Bell Polynomials ◽  
Genocchi Numbers ◽  
Central Factorial Numbers ◽  
Degenerate Bernstein Polynomials

In this paper, we firstly consider extended degenerate central factorial numbers of the second kind and provide some properties of them. We then introduce unified degenerate central Bell polynomials and numbers and investigate many relations and formulas including summation formula, explicit formula and derivative property. Moreover, we derive several correlations for the fully degenerate central Bell polynomials associated with the degenerate Bernstein polynomials and the degenerate Bernoulli, Euler and Genocchi numbers.

scholarly journals On Central Complete and Incomplete Bell Polynomials I

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 288 ◽  
Author(s):  
Taekyun Kim ◽  
Dae Kim ◽  
Gwan-Woo Jang
Keyword(s):  
Bell Polynomials ◽  
Explicit Formulas ◽  
Central Factorial Numbers

In this paper, we introduce central complete and incomplete Bell polynomials which can be viewed as generalizations of central Bell polynomials and central factorial numbers of the second kind, and also as ’central’ analogues for complete and incomplete Bell polynomials. Further, some properties and identities for these polynomials are investigated. In particular, we provide explicit formulas for the central complete and incomplete Bell polynomials related to central factorial numbers of the second kind.

scholarly journals On Degenerate Truncated Special Polynomials

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 144 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Bernstein Polynomials ◽  
Stirling Numbers ◽  
Bell Polynomials ◽  
Euler Polynomials ◽  
Exponential Polynomials ◽  
Special Polynomials ◽  
Summation Formulas ◽  
Special Cases ◽  
Proof Techniques

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.

scholarly journals Degenerate Bernstein polynomials

1983 ◽  
Vol 39 (1) ◽  
pp. 89-92 ◽  
Author(s):  
David Freedman ◽  
Eli Passow
Keyword(s):  
Bernstein Polynomials ◽  
Degenerate Bernstein Polynomials

scholarly journals Novel Identities for -Genocchi Numbers and Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Serkan Araci
Keyword(s):  
Bernstein Polynomials ◽  
Bernoulli Numbers ◽  
Genocchi Numbers

The essential aim of this paper is to introduce novel identities forq-Genocchi numbers and polynomials by using the method by T. Kim et al. (article in press). We show that these polynomials are related top-adic analogue of Bernstein polynomials. Also, we derive relations betweenq-Genocchi andq-Bernoulli numbers.

scholarly journals On r-Central Incomplete and Complete Bell Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 724 ◽  
Author(s):  
Dae San Kim ◽  
Han Young Kim ◽  
Dojin Kim ◽  
Taekyun Kim
Keyword(s):  
Stirling Numbers ◽  
Bell Polynomials ◽  
Explicit Formulas ◽  
Central Factorial Numbers

Here we would like to introduce the extended r-central incomplete and complete Bell polynomials, as multivariate versions of the recently studied extended r-central factorial numbers of the second kind and the extended r-central Bell polynomials, and also as multivariate versions of the r- Stirling numbers of the second kind and the extended r-Bell polynomials. In this paper, we study several properties, some identities and various explicit formulas about these polynomials and their connections as well.

scholarly journals On degenerate central complete bell polynomials

2019 ◽  
Vol 13 (3) ◽  
pp. 805-818
Author(s):  
Taekyun Kim ◽  
San Kim ◽  
Gwan-Woo Jang
Keyword(s):  
Bell Polynomials ◽  
Explicit Formulas ◽  
Central Factorial Numbers

In this paper, we consider of generalized central complete and incomplete Bell polynomials called degenerate central complete and incomplete Bell polynomials. These polynomials are generalizations of the recently introduced central complete Bell polynomials and `degenerate' analogues for the central complete and incomplete Bell polynomials. We investigate some properties and identities for these polynomials. Especially, we give explicit formulas for the degenerate central complete and incomplete Bell polynomials related to degenerate central factorial numbers of the second kind.

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