Related papers: Integrable pseudopotentials related to generalized…
Many product formulas are known classically for generalized hypergeometric functions over the complex numbers. In this paper, we establish some analogous formulas for generalized hypergeometric functions over finite fields.
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
By analogy to the theory of harmonic fields on the complex plane, we build the theory of wave-like fields on the plane of double variable. We construct the hyperbolic analogues of point vortices, sources, vortice-sources and their…
It is known that a large class of integrable hydrodynamic type systems can be constructed through the Lauricella function, a generalization of the classical Gauss hypergeometric function. In this paper, we construct novel class of…
In this paper, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and develop some transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
A relationship between two old mathematical subjects is observed: the theory of hypergeometric functions and the separability in classical mechanics. Separable potential perturbations of the integrable billiard systems and the Jacobi…
In this work we consider superintegrable systems in the classical $r$-matrix method. By using other authomorphisms of the loop algebras we construct new superintegrable systems with rational potentials from geodesic motion on $R^{2n}$.
The contact interaction is often used in modeling ultracold atomic gases, although it leads to pathological behavior arising from the divergence of the many-body wavefunction when two particles coalesce. This makes it difficult to use this…
This article is a contribution to the classification of quadratically integrable systems with vector potentials whose integrals are of the nonstandard, nonseparable type. We focus on generalized parabolic cylindrical case, related to…
We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.
The consistency between the exchange-correlation functional used in pseudopotential construction and in the actual density functional theory calculation is essential for the accurate prediction of fundamental properties of materials.…
We discuss $5d$ and $6d$ supersymmetric gauge theories in the target-space with compactified directions and with the matter hypermultiplets in fundamental representations in the framework of integrable systems. In particular, we consider…
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
In this paper, a new two-dimensional Hardy type inequality is given in terms of pseudo-analysis dealing with set-valued functions. The first one is given for a pseudo-integral of set-valued function where pseudo-addition and…
We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using…
We study a class of one-dimensional classical fluids with penetrable particles interacting through positive, purely repulsive, pair-potentials. Starting from some lower bounds to the total potential energy, we draw results on the…
The pseudospherical functions on one-sheet, two-dimensional hyperboloid are discussed. The simplest method of construction of these functions is introduced using the Fock space structure of the representation space of the su(1,1) algebra.…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…