Related papers: Hypergeometric type functions and their symmetries
This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as…
We give a new method to prove in a uniform and easy way various transformation formulas for Gauss hypergeometric functions. The key is Jacobi's canonical form of the hypergeometric differential equation. Analogy for $q$-hypergeometric…
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…
Integral relations with the Cauchy kernel on a semi-axis for the Laguerre polynomials, the confluent hypergeometric function, and the cylindrical functions are derived. A part of these formulas is obtained by exploiting some properties of…
We investigate a relation between the Mordell-Tornheim type of multiple Dirichlet series and a confluent hypergeometric function. We prove it by applying the Mellin-Barnes integral formula. Also, main results in this paper contain two kinds…
The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention is devoted to existing techniques for the construction of the $\epsilon$-expansion. As an example, we present a detailed discussion of…
Several new relationships between hypergeometric functions are found by comparing results for Feynman integrals calculated using different methods. A new expression for the one-loop propagator-type integral with arbitrary masses and…
We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized…
We develop an underlying relationship between the theory of rational approximations and that of isomonodromic deformations. We show that a certain duality in Hermite's two approximation problems for functions leads to the Schlesinger…
A new class of harmonic Hadamard manifolds, those spaces called of hypergeometric type, is defined in terms of Gauss hypergeometric equations. Spherical Fourier transform defined on a harmonic Hadamard manifold of hypergeometric type admits…
We investigate the symmetric Dunkl-classical orthogonal polynomials by using a new approach applied in connection with the Dunkl operator. The main aim of this technique is to determine the recurrence coefficients first and foremost. We…
We develop a notion of rank one properly convex domains (or Hilbert geometries) in the real projective space. This is in the spirit of rank one non-positively curved Riemannian manifolds and CAT(0) spaces. We define rank one isometries for…
We construct several expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two variables of the fist kind. The coefficients of different…
We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which…
The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.
We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum…
In this paper, we aim to obtain a representation of Humbert's hy- pergeometric function in a series of Gauss's function 2F1. A few interesting results have also been deduced as special case of our main findings.
Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product…
The geometry of (2,1) supersymmetric sigma-models is reviewed and the conditions under which they have isometry symmetries are analysed. Certain potentials are constructed that play an important role in the gauging of such symmetries. The…
We prove new integral formulas for generalized hypergeometric functions and their confuent variants. We apply them, via stationary phase formula, to study WKB expansions of solutions: for large argument in the confuent case and for large…