Related papers: $q$-Identities related to overpartitions and divis…
We will prove an identity involving refined $q$-trinomial coefficients. We then extend this identity to two infinite families of doubly bounded polynomial identities using transformation properties of the refined $q$-trinomials in an…
We present new proofs and generalizations of unimodality of the q-binomial coefficients \binom{n}{k}_q as polynomials in q. We use an algebraic approach by interpreting the differences between numbers of certain partitions as Kronecker…
In 1954, Atkin and Swinnerton-Dyer proved Dyson's conjectures on the rank of a partition by establishing formulas for the generating functions for rank differences in arithmetic progressions. In this paper, we prove formulas for the…
In this paper we develop a method to calculate the overpartition function efficiently using a Hardy-Rademacher-Ramanujan type formula, and we use this method to find many new Ramanujan-style congruences, whose existence is predicted by…
This object of this paper to give several properties and applications of multiple p-adic q-L-function of two variables.
In this paper, we combined two types of partitions and introduced 2-colored Rogers-Ramanujan partitions. By finding some functional equations and using a constructive method, some identities have been found. Some Overpartition identities…
Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ${\tilde {\partial}}$-equations are studied. More generally functions of several…
Integer partitions have long been of interest to number theorists, perhaps most notably Ramanujan, and are related to many areas of mathematics including combinatorics, modular forms, representation theory, analysis, and mathematical…
This paper addresses the study and applications of polyhedral duality of locally convex topological vector (LCTV) spaces. We first revisit the classical Rockafellar's proper separation theorem for two convex sets one which is polyhedral and…
In this note, we present a curious $q$-series identity with applications to certain partitions with bounded part differences.
We deliver here second new $\textit{H(x)}-binomials'$ recurrence formula, were $H(x)-binomials' $ array is appointed by $Ward-Horadam$ sequence of functions which in predominantly considered cases where chosen to be polynomials . Secondly,…
In this paper, we consider sums related the floor function. We can improve some previous results for some special arithmetic functions considered by Bordell\'es [3], Stucky[9] and Liu-Wu-Yang [6]. We can also give a refined result for…
Recently, Wang and Ma propose a conjecture associated with the possible generalization of Andrews-Warnaar identities. It is confirmed in this paper. As the applications of this conjecture, we prove that a family of series can be expressed…
Given the growing quantity of proposals and works of basic hypergeometric functions in the scope of $q$-calculus, it is important to introduce a systematic classification of $q$-calculus. Our aim in this article is to investigate certain…
We prove some results related to a conjecture of Hivert and Thi\'ery about the dimension of the space of q-harmonics. In the process we compute the actions of the involved operators on symmetric and alternating functions, which have some…
It is shown that the duals of several categories of topological flavour, like the categories of ordered sets, generalised metric spaces, probabilistic metric spaces, topological spaces, approach spaces, are quasivarieties, presenting a…
After obtaining some useful identities, we prove an additional functional relation for $q$ exponentials with reversed order of multiplication, as well as the well known direct one in a completely rigorous manner.
Using $q$-calculus we study a family of reproducing kernel Hilbert spaces which interpolate between the Hardy space and the Fock space. We give characterizations of these spaces in terms of classical operators such as integration and…
We give three elementary proofs of a nice equality of definite integrals, which arises from the theory of bivariate hypergeometric functions, and has connections with irrationality proofs in number theory. We furthermore provide a…
We give a commutative algebra viewpoint on Andrews recursive formula for the partitions appearing in "Gordon's identities", which are a generalization of Rogers-Ramanujan identities. Using this approach and differential ideals we conjecture…