Related papers: Identities between q-hypergeometric and hypergeome…
In this paper, a general integral identity for a twice differentiable functions is derived. By using of this identity, the author establishes some new Hermite-Hadamard type and Simpson type inequalities for differentiable…
In this paper, we derive eight basic identities of symmetry in three variables related to $q$-Bernoulli polynomials and the $q$-analogue of power sums. These and most of their corollaries are new, since there have been results only about…
In this work we investigate the complex Leibniz superalgebras with characteristic sequence $(n-1, 1 | m_1, ..., m_k)$ and with nilindex equal to $n+m.$ We prove that such superalgebras with the condition $m_2\neq0$ have nilindex less than…
In this work, we derive relations between generating functions of double stuffle relations and double shuffle relations to express the alternating double Euler sums $\zeta\left(\overline{r}, s\right)$, $\zeta\left(r, \overline{s}\right)$…
Since the study by Jacobi and Hecke, Hecke-type series have received a lot of attention. Unlike such series associated with indefinite quadratic forms, identities on Hecke-type series associated with definite quadratic forms are quite rare…
It is known that solutions of the KZ equations can be written in the form of multidimensional hypergeometric integrals. In 2017 in a joint paper of the author with V. Schechtman the construction of hypergeometric solutions was modified, and…
Recently N.Jing discovered a certain combinatorial identity from validity of the Serre relations in some vertex representations of quantum Kac-Moody algebras. We generalize this identity, in particular, extending it from polynomials to…
We derive the multiplicative duality "q<->1/q" and other typical mathematical structures as the special cases of the (mu,nu,q)-relation behind Tsallis statistics by means of the (mu,nu)-multinomial coefficient. Recently the additive duality…
I obtain new evaluations of special values of multiple polylogarithms by using a limiting case of a basic hypergeometric identity of G. E. Andrews.
In this paper, first we prove that all finite dimensional special Heisenberg Lie superalgebras with even center have same dimension, say $(2m+1\mid n)$ for some non-negative integers $m,n$ and are isomorphism with them. Further, for a…
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…
The Cayley-Hamilton-Newton theorem - which underlies the Newton identities and the Cayley-Hamilton identity - is reviewed, first, for the classical matrices with commuting entries, second, for two q-matrix algebras, the RTT-algebra and the…
It is well-known that differentiation of hypergeometric function multiplied by a certain power function yields another hypergeometric function with a different set of parameters. Such differentiation identities for hypergeometric functions…
We present a novel framework for studying combinatorial identities through the geometric lens of subset distributions in q-valued cubes. By analyzing how elements of arbitrary subsets are distributed among the faces of the cube E_q^n, we…
A new Hilbert-type integral inequality in the whole plane with the non-homogeneous kernel and parameters is given. The constant factor related to the hypergeometric function and the beta function is proved to be the best possible. As…
This paper continues an earlier research of the authors on universal quadratic identities (QIs) on minors of quantum matrices. We demonstrate situations when the universal QIs are provided, in a sense, by the ones of four special types…
Explicit separability of general two qubits density matrices is related to Lorentz transformations. We use the 4-dimensional form R(u,v=0,1,2,3) of the Hilbert-Schmidt (HS) decomposition of the density matrix. For the generic case in which…
Let $\mathfrak q$ be a Lie algebra over a field $\mathbb K$ and $p,\tilde p\in\mathbb K[t]$ two different normalised polynomials of degree at least 2. As vector spaces both quotient Lie algebras $\mathfrak q[t]/(p)$ and $\mathfrak…
A Lie algebra $L$ of dimension $n \ge1 $ may be classified, looking for restrictions of the size on its second integral homology Lie algebra $H_2(L,\mathbb{Z})$, denoted by $M(L)$ and often called Schur multiplier of $L$. In case $L$ is…
The well-known Kummer's formula evaluates the hypergeometric series 2F1(A,B;C;-1) when the relation B-A+C=1 holds. This paper deals with evaluation of 2F1(-1) series in the case when C-A+B is an integer. Such a series is expressed as a sum…