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Some identities of Chebyshev polynomials are deduced from Waring's formula on symmetric functions. In particular, these formulae generalize some recent results of Grabner and Prodinger.

Combinatorics · Mathematics 2007-05-23 Jiang Zeng , Jin Zhou

In this paper, we consider the degenerate Frobenius-Euler polynomials and investigate some identities of these polynomials.

Number Theory · Mathematics 2015-07-20 Taekyun Kim , Hyuck-In Kwon , Jong-Jin Seo

In this paper, we consider higher-order Bernoulli and poly-Bernoulli mixed type polynomials and we give some interesting identities of those polynomials arising from umbral calculus.

Number Theory · Mathematics 2013-07-09 Dae San Kim , Taekyun Kim

In this paper, we give some recurrence formula and new and interesting identities for the poly-Bernoulli numbers and polynomials which are derived from umbral calculus.

Number Theory · Mathematics 2013-07-01 Dae san Lom , Taekyun Kim

Using generating functions, we derive many identities involving balancing and Lucas-balancing polynomials. By relating these polynomials to Chebyshev polynomials of the first and second kind, and Fibonacci and Lucas numbers, we offer some…

Number Theory · Mathematics 2020-07-29 Robert Frontczak , Taras Goy

In this paper, we will deal with some new formulae for two product Genocchi polynomials together with both Euler polynomials and Bernoulli polynomials. We get some applications for Genocchi polynomials. Our applications possess a number of…

Number Theory · Mathematics 2019-07-04 Serkan Araci , Mehmet Acikgoz , Erdoğan Şen

Recently, Kim-Jang-Yi have introduced q-Bernstein polynomials. From these q-Berstein polynomials, we investigte some properties related to q-Stirling numbes and q-Bernoulli numbes.

Number Theory · Mathematics 2010-06-11 Taekyun Kim , Jongsung Choi , Young-Hee Kim

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

The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.

Mathematical Physics · Physics 2007-05-23 Carl M. Bender , Dorje C. Brody , Bernhard K. Meister

In this paper, we give a fermionic p-adic integral representions of Benstein polynomials associated with Euler numbers and polynomials. Finally, we give some interesting identities for the Euler numbers by using the properties of our…

Number Theory · Mathematics 2010-09-01 T. Kim , J. Choi , Y. H. Kim , C. S. Ryoo

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

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

In this overview paper a direct approach to q-Chebyshev polynomials and their elementary properties is given. Special emphasis is placed on analogies with the classical case. There are also some connections with q-tangent and q-Genocchi…

Combinatorics · Mathematics 2012-07-27 Johann Cigler

In this paper, we consider linear differential equations satisfied by the generating function for Hermite polynomials and derive some new identities involving those polynomials.

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

We express the N\"{o}rlund polynomials in terms of the second-order Eulerian numbers. Based on this expression, we derive several identities related to the Bernoulli numbers. In particular, we present a short proof of the problem raised by…

Combinatorics · Mathematics 2021-04-21 Amy M. Fu

In this paper, we study some properties of Euler polynomials arising from umbral calculus. Finally, we give some interesting identities of Euler polynomials using our results. Recently, Dere and Simsek have studied umbral calculus related…

Number Theory · Mathematics 2012-11-29 Dae San Kim , Taekyun Kim , Seog-Hoon Rim

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

In this paper, we study some symmetric identities of q-Euler numbers and polynomials. From these properties, we derive several identities of q-Euler numbers and polynomials.

Number Theory · Mathematics 2013-10-08 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 paper we give some interesting relationships between twisted (h,q)-Euler numbers and q-Berstein polynomnials by using fermionic p-adic q-integrals on Zp

Number Theory · Mathematics 2011-05-03 D. V. Dolgy , D. J. Kang , T. Kim , B. Lee