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Related papers: On Multi Poly-Bernoulli Polynomials

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In this paper, we consider various speical mixed-type polynomials which are related to Bernoulli, Euler, Changhee and Daehee polynomials. From those polynomials, we derive some interesting and new identities

Number Theory · Mathematics 2014-06-10 Dae San Kim , Taekyun Kim , Hyucj In Kwon

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

In this paper, some formulae for Genoochi polynomials of higher order are derived using the fact that sets of Bernoulli and Euler polynomials of higher order form basis for the polynomial space.

Classical Analysis and ODEs · Mathematics 2020-09-09 Cristina B. Corcino , Roberto B. Corcino , Joy Ann A. Canete

In this paper we study q-Bernoulli numbers and polynomials related to q-Stirling numbers. From thsese studying we investigate some interesting q-stirling numbers' identities related to q-Bernoulli numbers.

Number Theory · Mathematics 2007-10-29 Taekyun Kim

Studying degenerate versions of various special polynomials have become an active area of research and yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of polylogarithm function, called…

Number Theory · Mathematics 2020-02-12 Taekyun Kim , Dae San Kim

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

In this paper we investigate some interesting formulae of q-Euler numbers and polynomials related to the modified q-Bernstein polynomials.

Number Theory · Mathematics 2010-07-21 Min-soo Kim , Daeyeoul Kim , Taekyun Kim

We define $q$-poly-Bernoulli polynomials $B_{n,\rho,q}^{(k)}(z)$ with a parameter $\rho$, $q$-poly-Cauchy polynomials of the first kind $c_{n,\rho,q}^{(k)}(z)$ and of the second kind $\widehat c_{n,\rho,q}^{(k)}(z)$ with a parameter $\rho$…

Number Theory · Mathematics 2021-03-01 Takao Komatsu

The Cauchy polynomials with a $q$ parameter were recently defined, and several arithmetical properties were studied. In this paper, we establish explicit formulae for computing the Cauchy polynomials with a $q$ parameter in terms of…

Combinatorics · Mathematics 2018-04-17 F. A. Shiha

Recently, Komastu introduced the concept of poly-Cauchy numbers and polynomials which generalize Cauchy numbers and polynomials. In this paper, we introduce new generaliza- tion of poly-Cauchy and poly-Bernoulli numbers and polynomials.…

Combinatorics · Mathematics 2014-10-21 B. S. El-Desouky , R. S. Gomaa

In this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus to have…

Number Theory · Mathematics 2013-02-22 Taekyun Kim , Dae San Kim , Seog-Hoon Rim , Dmitry v. Dolgy

In this paper, we investigate new class of sequences related to fully degenerate Bernoulli numbers and polynomials. From those sequences, we derive some formulae for the degenerate Bernoulli and Euler polynomials.

Number Theory · Mathematics 2022-03-09 Taekyun Kim , Dae san Kim

New methods for derivation of Bell polynomials of the second kind are presented. The methods are based on an ordinary generating function and its composita. The relation between a composita and a Bell polynomial is demonstrated. Main…

Combinatorics · Mathematics 2011-09-09 Vladimir Kruchinin

In this paper we give some relation involving values of q-Bernoulli, q-Euler and Bernstein polynomials. From these relations, we obtain some interesting identities on the q-Bernoulli, q-Euler and Bernstein polynomials.

Number Theory · Mathematics 2015-05-27 A. Bayad , T. Kim

The relations between the Bernoulli and Eulerian polynomials of higher order and the complete Bell polynomials are found that lead to new identities for the Bernoulli and Eulerian polynomials and numbers of higher order. General form of…

Number Theory · Mathematics 2009-11-17 Boris Y. Rubinstein

In this paper, we introduce the degenerate multiple polyexponential functions which are multiple versions of the degenerate modified polyexponential functions. Then we consider the degenerate multi-poly-Genocchi polynomials which are…

Number Theory · Mathematics 2020-05-18 Taekyun Kim , Dae San Kim , Han Young kim , Jongkyum Kwon

By using the associated and restricted Stirling numbers of the second kind, we give some generalizations of the poly-Bernoulli numbers. We also study their arithmetical and combinatorial properties. As an application, at the end of the…

Number Theory · Mathematics 2015-10-26 Takao Komatsu , Kalman Liptai , István Mező

We study the q-analogue of Euler-Maclaurin formula and by introducing a new q-operator we drive to this form. Moreover, approximation properties of q-Bernoulli polynomials is discussed. We estimate the suitable functions as a combination of…

Classical Analysis and ODEs · Mathematics 2017-11-06 Mohammad Momenzadeh , Ibrahim Yusuf Kakangi

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

The aim of this paper is to investigate generating functions for modification of the Milne-Thomson's polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. By applying the Umbral algebra to these generating…

Classical Analysis and ODEs · Mathematics 2018-11-19 Rahime Dere , Yilmaz Simsek