Related papers: Variants of $q$-hypergeometric equation
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
We extend the holographic formula for the critical $Q$-curvature to all $Q$-curvatures.
The direct or algorithmic approach for the Jacobian problem, consisting of the direct construction of the inverse polynomials is proposed. The so called principle and derived Jacobi conditions are proposed and discussed. The algorithmic…
We study the following variant of the Erd\H{o}s distance problem. Given $E$ and $F$ a point sets in $\mathbb{R}^d$ and $p = (p_1, \ldots, p_q)$ with $p_1+ \cdots + p_q = d$ is an increasing partition of $d$ define $$ B_p(E,F)=\{(|x_1-y_1|,…
We consider the possibility to use the areas of two-simplexes, instead of lengths of edges, as the dynamical variables of Regge calculus. We show that if the action of Regge calculus is varied with respect to the areas of two-simplexes, and…
In this article, the 2-iterated q-Appell family is introduced. Certain 2-iterated q-Appell and mixed type q-special polynomials are considered as members of this family. The numbers related to these polynomials are obtained. The determinant…
Original English Summary. - A systematic method of constructing potentials, for which the one-variable Schroedinger equation can be solved in terms of the hypergeometric (HGM) function, is presented. All the potentials, obtained by…
We study quasilinear elliptic double obstacle problems with a variable exponent growth when the right-hand side is a measure. A global Calder\'{o}n-Zygmund estimate for the gradient of an approximable solution is obtained in terms of the…
Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex…
We derive parametric travelling-wave solutions of non-linear QCD equations. They describe the evolution towards saturation in the geometric scaling region. The method, based on an expansion in the inverse of the wave velocity, leads to a…
Recently, the so-called Hermite-Hadamard inequality for (operator) convex functions with one variable has known extensive several developments by virtue of its nice properties and various applications. The fundamental target of this paper…
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 first show how one can obtain Al-Salam--Chihara polynomials, continuous dual $q$-Hahn polynomials, and Askey--Wilson polynomials from the little $q$-Laguerre and the little $q$-Jacobi polynomials by using special transformations. This…
By solving an infinite nonlinear system of $q$-difference equations one constructs a chain of $q$-difference operators. The eigenproblems for the chain are solved and some applications, including the one related to $q$-Hahn orthogonal…
We prove some Rodriguez-Villegas type congruences for truncated q-hypergeometric functions.
We establish some new generalizations of Erd\H{o}s-Mordell inequality by adding weights to its terms. Using these generalizations, we derived strengthened versions of the original Erd\H{o}s-Mordell inequality. We also found two other…
This object of this paper to give several properties and applications of multiple p-adic q-L-function of two variables.
Limiting cases are studied of the Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials. We recover recently and not so recently introduced families of hypergeometric orthogonal polynomials in several variables…
We study the existence of formal power series solutions to q-algebraic equations. When a solution exists, we give a sufficient condition on the equation for this solution to have a positive radius of convergence. We emphasize on the case…
This article shows how to find the solution of an arbitrary quintic equation by performing two simultaneous folds on a sheet of paper. The folds achieve specific incidences between a set of points and lines that are determined by the…