Related papers: On q-Berstein and q-Hermite polynomials
Recently, Boole polynomials have been studied by Kim and Kim over the p-adic number field. In this paper, we consider a q-extension of Boole polynomials by using the fermionic p-adic integrals on Zp and give some new identities related to…
The q-classical orthogonal polynomials of the q-Hahn Tableau are characterized from their orthogonality condition and by a first and a second structure relation. Unfortunately, for the q-semiclassical orthogonal polynomials (a…
We describe a congruence property of solvable polynomials over Q, based on the irreducibility of cyclotomic polynomials over number fields that meet certain conditions.
In this study, the new algebraic properties related to bivariate Fibonacci polynomials has been given. We present the partial derivatives of these polynomials in the form of convolution of bivariate Fibonacci polynomials. Also, we define a…
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…
The continuous big $q$-Hermite polynomials are shown to realize a basis for a representation space of an extended $q$-oscillator algebra. An expansion formula is algebraically derived using this model.
We summarize results concerning the Bernstein property of differential equations.
The purpose of this paper is to give symmetric identities for higher-order degenerate q- Bernoulli polynomials arising from the p-adic q-integral on Zp.
In this note, we shall provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence formulas.
Recently, Kim-Kim Introduced some interesting identities of symmetry for q-Bernoulli polynomials under symmetry group of degree n. In this paper, we study the degenerate q-Euler polynomials and derive some identities of symmetry for these…
Eisenstein polynomials, which were defined by the second author, are analogues of the concept of an Eisenstein series. The second author conjectured that there exist some analogous properties between Eisenstein series and Eisenstein…
In this paper, we give some new identities of symmetry for q-Bernoulli polynomials under the symmetric group of degree n arising from p-adic q-integrals on Zp.
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.
In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and investigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate…
We consider the Witt-type formula for Daehee numbrers and polynomials and investigate some properties of those numbers and polynomials. In particular, Daehee numbers are closely related to higher-order Bernoulli numbers and Bernoulli…
In this paper we shall evaluate two alternating sums of binomial coefficients by a combinatorial argument. Moreover, by combining the same combinatorial idea with partition theoretic techniques, we provide $q$-analogues involving the…
In this paper, we construct the alternating multiple q-zeta function(= Multiple Euler q-zeta function) and investigate their properties. Finally, we give some interesting functional eauations related to q-Euler polynomials.
We introduce a class of doubly indexed real Hermite polynomials and we deal with their related properties like the associated recurrence formulae, Runge's addition formula, generating function and Nielsen's identity.
We derive inversion formulas involving orthogonal polynomials which can be used to find coefficients of differential equations satisfied by certain generalizations of the classical orthogonal polynomials. As an example we consider special…
In this paper we present several natural $q$-analogues of the poly-Bernoulli numbers arising in combinatorial contexts. We also recall some relating analytical results and ask for combinatorial interpretations.