Related papers: A note on the generalized q-Euler numbers(2)
In the paper, we generalize some congruences of Lehmer for general composite numbers.
In this paper we consider the extended q-Bernstein polynomials which are constructed by T. Kim and we investigate some properties.
In the present paper we generalize the Eulerian numbers (also of the second and third orders). The generalization is connected with an autonomous first-order differential equation, solutions of which are used to obtain integral…
Carlitz has introduced an interesting $q$-analogue of Frobenius-Euler numbers in [4]. He has indicated a corresponding Stadudt-Clausen theorem and also some interesting congruence properties of the $q$-Euler numbers. In this paper we give…
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…
Using Eulerian and Euler numbers, we establish congruences concerning sums involving harmonic numbers, tangent numbers and Genocchi numbers.
In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.
In this paper we present the generalization of the higher order q-Euler numbers and q-Genocchi numbers and w-Genocchi numbers and polynomials of high order using the multivariate fermionic p-adic integral on Zp. We have the interpolation…
We study the explicit formula of Euler numbers and polynomials of higher order
We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and…
In this article, we introduce combinatorial models for poly-Bernoulli polynomials and poly-Euler numbers of both kinds. As their applications, we provide combinatorial proofs of some identities involving poly-Bernoulli polynomials.
In the present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give…
In this paper we construct $q$-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the $q$-analogue of alternating sums of powers of consecutive integers due to Euler.
We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.
In this paper we investigate the properties of the Euler functions. By using the Fourier transform for the Euler function, we derive the interesting formula related to the infinite series. Finally we give some interesting identities between…
In this paper we state some conjectures about q-Fibonacci polynomials which for q=1 reduce to well-known results about Fibonacci numbers and Fibonacci polynomials.
In this paper we consider the q-extension of the generating function for the higher-order generalized Genocchi numbers and polynomials attached to Dirichlet's character.
Many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This…
We present a relationship between the generalized hyperharmonic numbers and the poly-Bernoulli polynomials, motivated from the connections between harmonic and Bernoulli numbers. This relationship yields numerous identities for the…
Starting with some determinants of binomial coefficients which are related to Fibonacci and Lucas polynomials we study similar determinants for some generalizations of these polynomials and their q-analogues.