相关论文: A note on the sums of powers of consecutive q-inte…

In this paper we construct the $q$-analogue of Barnes's Bernoulli numbers and polynomials of degree 2, for positive even integers, which is an answer to a part of Schlosser's question. For positive odd integers, Schlosser's question is…

Following an idea due to J. Bernoulli, we explore the q-analogue of the sums of powers of consecutive integers.

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 give the q-analogue of the sums of the n-th powers of positive integers up to k-1.

In this paper we construct a new q-Euler numbers and polynomials. By using these numbers and polynomials, we give the interesting formulae related to alternating sums of powers of consecutive q-integers following an idea due to Euler.

We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.

In this paper, we investigate a specific class of $q$-polynomial sequences that serve as a $q$-analogue of the classical Appell sequences. This framework offers an elegant approach to revisiting classical results by Carlitz and, more…

In this paper, we construct the new $q$-analogue of the ordinary Euler numbers and polynomials by using the $q$-Volkenborn integrals.

A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…

By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.

We show that Genocchi and Bernoulli numbers are closely related to Fibonacci polynomials and derive some q-analogues.

We derive some q-analogs of Euler-Cassini-type identities and of recurrence formulas for powers of Fibonacci polynomials.

The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli polynomials and Euler polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the…

The main purpose of this paper is to introduce and investigate a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials. The $q$-analogues of well-known formulas are derived. The $q$-analogue of the Srivastava--Pint\'er addition…

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

Let $$ S_{m,n}(q):=\sum_{k=1}^{n}\frac{1-q^{2k}}{1-q^2} (\frac{1-q^k}{1-q})^{m-1}q^{\frac{m+1}{2}(n-k)}. $$ Generalizing the formulas of Warnaar and Schlosser, we prove that there exist polynomials $P_{m,k}(q)\in\mathbb{Z}[q]$ such that $$…

In this work, the q-analogue of Bernoulli inequality is proved. Some other related results are presented.

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…

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.

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.