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Related papers: Some new properties on degenerate Bell polynomials

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Departing from a class of infinite series with central binomial coefficients in the numerator and depending on a positive integer parameter, we first extend known identities to all complex parameters. Then we use various methods, including…

Number Theory · Mathematics 2025-11-04 Karl Dilcher , Christophe Vignat

In recent years, studying degenerate versions of various special polynomials and numbers have attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Bernoulli polynomials and…

Number Theory · Mathematics 2019-03-12 Dae San Kim , Han Young Kim , Sung-Soo Pyo , Taekyun Kim

In this paper, we study some properties of associated sequaences in umbral calculus. From these properties, we derive new and interesting identities of several kinds of polynomials.

Number Theory · Mathematics 2012-11-19 Dae San Kim , Taekyun Kim , Seog-Hoon Rim

Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. We consider the probabilistic bivariate Bell polynomials associated with Y and the probabilistic bivariate r-Bell polynomials associated…

Number Theory · Mathematics 2024-03-26 Taekyun Kim , Dae san Kim

In this paper, we consider the q-extensions of Boole polynomials. From those polynomials, we derive some new and interesting properties and identities related to special polynomials.

Number Theory · Mathematics 2014-03-19 Dae San Kim , Taekyun Kim , Jong Jin Seo

We introduce a new sequence of unsigned degenerate Stirling numbers of the first kind. Following the work of Adell-Lekuona, who represented unsigned Stirling numbers of the first kind as multiples of the expectations of specific random…

Number Theory · Mathematics 2025-09-04 Taekyun Kim , Dae san Kim , Kyo-Shin Hwang , Dmitry V. Dolgy

We study a class of bivariate deformed Hermite polynomials and some of their properties using classical analytic techniques and the Wigner map. We also prove the positivity of certain determinants formed by the deformed polynomials. Along…

Mathematical Physics · Physics 2014-10-21 S. Twareque Ali , Mourad E. H. Ismail , Nurisya M. Shah

The purpose of this article is to introduce q-deformed Stirling numbers of the first and second kinds. Relations between these numbers, Riemann zeta function and q-Bernoulli numbers of higher order are given. Some relations related to the…

Number Theory · Mathematics 2018-05-16 Yilmaz Simsek

In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials

Rings and Algebras · Mathematics 2024-03-19 Alina G. Goutor , Sergey V. Tikhonov

In this paper, we study linear differential equations arising from Bessel polynomials and their applications. From these linear differential equations, we give some new and explicit identities for Bessel polynomials.

Number Theory · Mathematics 2016-10-04 Taekyun Kim , Dae san Kim

We introduce a notion of tangential Alexander polynomials for plane curves and study the relation with $\theta$^Alexander polynomial. As an application, we use these polynomials to study a non-reduced degeneration $C_t \to D_0+jL$. We show…

Algebraic Geometry · Mathematics 2007-05-23 Mutsuo Oka

The purpose of this paper is to present a syatemic study of some familes of higher-order Euler numbers and polynomials. In particular, by using the basis property of higher-order Euler polynomials for the space of polynomials of degree less…

Number Theory · Mathematics 2012-11-19 Dae San Kim , Taekyun Kim

In this article, we give an account of some recent irreducibility testing criteria for polynomials having integer coefficients over the field of rational numbers.

Number Theory · Mathematics 2023-10-05 Sanjeev Kumar , Jitender Singh

In this paper, we introduce bivariate polynomial sets of deformed $q$-Appell type, and we study the algebraic properties of these sets. We show the relation between deformed bivariate $q$-Appell polynomials and deformed homogeneous…

Combinatorics · Mathematics 2025-05-29 Ronald Orozco López

In this paper, we study some properties of Whitney numbers of Dowling lattices and related polynomials. We answer the following question: there is relation between Stirling and Eulerian polynomials. Can we find a new relation between…

Combinatorics · Mathematics 2012-12-06 Mourad Rahmani

We study inverse factorial series and their relation to Stirling numbers of the first kind. We prove a special representation of the polylogarithm function in terms of series with such numbers. Using various identities for Stirling numbers…

Number Theory · Mathematics 2022-06-15 Khristo N. Boyadzhiev

In this paper, we investigate the properties of q-Hermite polynomials related to q-Bernstein polynomials. From these properties, we derive some interesting relations between q-Berstein polynomials and q-Hermite polynomials.

Number Theory · Mathematics 2011-01-26 T. Kim , J. Choi , Y. H. Kim , C. S. Ryoo

We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and…

Combinatorics · Mathematics 2015-03-03 B. S. El-Desouky , Abdelfattah Mustafa

Several new estimates for the 2-adic valuations of Stirling numbers of the second kind are proved. These estimates, together with criteria for when they are sharp, lead to improvements in several known theorems and their proofs, as well as…

Number Theory · Mathematics 2019-12-04 Arnold Adelberg

In the paper, the author finds an explicit formula for computing Bell numbers in terms of Kummer confluent hypergeometric functions and Stirling numbers of the second kind.

Combinatorics · Mathematics 2014-09-11 Feng Qi