Related papers: q-Analogue of Gauss' Divisibility Theorem

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

We establish a q-analogue of Wolstenholme's harmonic series congruence.

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

We prove a new q-analogue of Nicomachus's Theorem about the sum of cubes and some related results.

A $q$-analogue of the multiple gamma functions is introduced, and is shown to satisfy the generalized Bohr-Morellup theorem. Furthermore we give some expressions of these function.

We give q-analogues of Wilson's theorem for the primes congruent 1 and 3 modulo 4 respectively. And q-analogues of two congruences due to Mordell and Chowla are also established.

We present a multivariable generalization of the digital binomial theorem from which a q-analog is derived as a special case.

In this paper, we consider a q-analogue of Laplace transform and we investigate some properties of q-Laplace transform. From our investigation, we derive some interesting formulae related to q-Laplace transform.

Andrews once gave $q$-analogues of a binomial congruence of Glaisher, and he suggested perfect $q$-analogues. In this note we give ones meeting the demand of Andrews.

This note gives a simple approach to q-analogues of some results associated with Abel polynomials.

In this paper, we present the (p; q)-analogues of some inequalities concerning the digamma function. Our results generalize some earlier results.

A few years ago, the concept of a D-analogue was introduced as a Dirichlet series analogue for the already known and well researched hypergeometric q-series. The D-analogue of the q-Dixon sum is given here, in the context of seeing a direct…

A q-difference analogue of the fourth Painlev\'e equation is proposed. Its symmetry structure and some particular solutions are investigated.

In this article we give a proof of a q-analogue of the celebrated four functions theorem. This analogue was conjectured by Bjorner and includes as special cases both the four functions theorem and also Bjorner's q-analogue of the FKG…

We construct a subalgebra of the Hecke algebra of type A. This is a generalization of the group algebra of the alternating groups. All the equivalent classes of irreducible representations of the subalgebra and the q-analogue of the…

We introduce a $q$-analog of the polyanalytic Bargmann transform on $\mathbb{C}$.

New results on comparison of distributions of Gaussian quadratic forms are presented

We generalize Pappus chain theorem and give an analogue to this theorem.

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…

We prove some special cases of Bergeron's inequality involving two Gaussian polynomials (or $q$-binomials).