Related papers: Hypergeometric identities related to Ruijsenaars s…

Source identities are fundamental identities between multivariable special functions. We give a geometric derivation of rational and trigonometric source identities. We also give a systematic derivation and extension of various determinant…

In this article we developed a special topic of our pure-mathematics papers concerning the hypergeometric theory. Based upon a Roberts's reduction approach of hyperelliptic integrals to elliptic ones and on the simultaneous multivariable…

Given complex numbers $m_1,l_1$ and nonnegative integers $m_2,l_2$, such that $m_1+m_2=l_1+l_2$, for any $a,b=0, ... ,\min(m_2,l_2)$ we define an $l_2$-dimensional Barnes type q-hypergeometric integral $I_{a,b}(z,\mu;m_1,m_2,l_1,l_2)$ and…

In this paper we give new identities involving q-Euler polynomials of higher order.

We introduce a new approach for the study of the Problem of Iterates using the theory on general ultradifferentiable structures developed in the last years. Our framework generalizes many of the previous settings including the Gevrey case…

We give an elementary proof of some identities that express the squares of Riemann zeta function at integer points in terms of the series involving hyperbolic functions, digamma function, Bernoulli numbers etc. In this version, inaccuracies…

We present some results and open problems related to expansions of the field of real numbers by hypergeometric and related functions focussing on definability and model completeness questions. In particular, we prove the strong model…

Here, we establish a polynomial identity in three variables $a, b, c$, and with the degree of the polynomial given in terms of two integers $L, M$. By letting $L$ and $M$ tend to infinity, we get the 1993 Alladi-Gordon $q$-hypergeometric…

We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.

We prove a family of $n$-th order identities for quantum $R$-matrices of Baxter-Belavin type in fundamental representation. The set of identities includes the unitarity condition as the simplest one ($n=2$). Our study is inspired by the…

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…

Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…

We give a combinatorial characterization of the identities holding in the semiring of all upper triangular Boolean $n\times n$-matrices and apply the characterization to computational complexity of identity checking, finite axiomatizability…

The superconformal index of a three-dimensional supersymmetric field theory can be expressed in terms of basic hypergeometric integrals. By comparing the indices of dual theories, one can find new integral identities for basic…

Leibniz algebras are non-skewsymmetric analogue of Lie algebras. In this paper, we consider weighted relative Rota-Baxter operators on Leibniz algebras. We define cohomology of such operators and as an application, we study their…

We discuss some aspects of the search for identities using computer algebra and symbolic methods. The focus is on so-called Apery-like formulae for special values of the Riemann Zeta function. Much work lays ahead in formally proving and…

We establish a determinant formula for the bilinear form associated with the elliptic hypergeometric integrals of type $BC_n$ by studying the structure of $q$-difference equations to be satisfied by them. The determinant formula is proved…

In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter systems. This…

We present a perturbative construction of two kinds of eigenfunctions of the commuting family of difference operators defining the elliptic Ruijsenaars system. The first kind corresponds to elliptic deformations of the Macdonald…

For Belavin's elliptic quantum R-matrix, we construct an L-operator as a set of difference operators acting on functions on the type A weight space. According to the fundamental relation $RLL=LLR$, the trace of the L-operator gives a…