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Related papers: Hermite and poly-Bernoulli mixed-type polynomials

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We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function and concepts of the Umbral Calculus associated with it. Also, we present…

Number Theory · Mathematics 2018-11-07 Orli Herscovici , Toufik Mansour

I recent years, many mathematicians studied various degenerate version of some spcial polynomials of which quite a few interesting results were discovered. In this paper, we introduce the type 2 degenerate Bernoulli polynomials of the…

Number Theory · Mathematics 2019-08-20 Taekyun Kim , Lee-Chae jang , Dae San Kim , Han-Young Kim

The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling…

Number Theory · Mathematics 2019-07-04 Serkan Araci , Mehmet Acikgoz , Hassan Jolany , Armen Bagdasaryan

In this paper, we consider degenerate poly-Bernoulli numbers and polynomials associated with polylogarithmic function and p-adic invariant integral on Zp. By using umbral calculus, we derive some identities of those numbers and polynomials

Number Theory · Mathematics 2015-06-11 Dae San Kim , Taekyun Kim

In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.

Combinatorics · Mathematics 2015-09-15 Feng Qi , Robin J. Chapman

The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate Stirling numbers of both kinds associated with degenerate hyperharmonic numbers and also with degenerate Bernolli, degenerate…

Number Theory · Mathematics 2023-04-05 Taekyun Kim , Dae San Kim

In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials

Number Theory · Mathematics 2013-02-21 Taekyun Kim , Dae San Kim , Seog-Hoon Rim , Dmitry V. Dolgy

Let P be the set of the sequence of polynomials of degree n. The aim of this paper is to study the Stirling numbers of the second kind associated with P and of the first kind associated with P, in a unified and systematic way with the help…

Number Theory · Mathematics 2022-02-24 Dae san Kim , taekyun Kim

We prove certain identities involving Euler and Bernoulli polynomials that can be treated as recurrences. We use these and also other known identities to indicate connection of Euler and Bernoulli numbers with entries of inverses of certain…

Rings and Algebras · Mathematics 2014-03-06 Paweł J. Szabłowski

In this paper, we characterize a duality relation between Eulerian recurrences and Eulerian recurrence systems, which generalizes and unifies Hermite-Biehler decompositions of several enumerative polynomials, including flag descent…

Combinatorics · Mathematics 2020-10-20 Shi-Mei Ma , Jun Ma , Jean Yeh , Yeong-Nan Yeh

In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.

Number Theory · Mathematics 2013-02-01 Taekyun Kim , Dae San Kim

In this paper we use probabilistic methods to derive some results on the generalized Bernoulli and generalized Euler polynomials. Our approach is based on the properties of Appell polynomials associated with uniformly distributed and…

Probability · Mathematics 2013-07-18 Bao Quoc Ta

Poly-Bernoulli numbers are one of generalizations of the classical Bernoulli numbers. Since a negative index poly-Bernoulli number is an integer, it is an interesting problem to study this number from combinatorial viewpoint. In this short…

Number Theory · Mathematics 2020-03-30 Toshiki Matsusaka

Using the methods of classical invariant theory a general approach to finding of identities for Bernulli, Euler and Hermite polynomials is proposed.

Combinatorics · Mathematics 2012-10-02 Leonid Bedratyuk

In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…

Number Theory · Mathematics 2014-01-28 Hassan Jolany , Mohsen Aliabadi , Roberto B. Corcino , M. R. Darafsheh

In this paper, we study higher-order Cauchy of the first kind and poly-Cauchy of the first kind mixed type polynomials with viewpoint of umbral calculus and give some interesting identities and formulae of those polynomials which are…

Number Theory · Mathematics 2013-08-12 Dae san Kim , Taekyun Kim

In this paper, we establish more identities of generalized multi poly-Euler polynomials with three parameters and obtain a kind of symmetrized generalization of the polynomials. Moreover, generalized multi poly-Bernoulli polynomials are…

Number Theory · Mathematics 2018-07-25 Roberto B. Corcino , Hassan Jolany , Cristina B. Corcino , Takao Komatsu

In this note, we shall provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence formulas.

Number Theory · Mathematics 2015-09-16 Su Hu , Min-Soo Kim

Many works have been done in recent years as to explorations for degenerate versions of some special polynomials and numbers, which began with the introduction of the degenerate Bernoulli and degenerate Euler polynomials by Carlitz. The aim…

Number Theory · Mathematics 2022-12-13 Taekyun Kim , Dae San Kim , Jongkyum Kwon

We give an expression of polynomials for higher sums of powers of integers via the higher order Bernoulli numbers.

Number Theory · Mathematics 2017-10-16 Andrei K. Svinin , Svetlana V. Svinina