Related papers: Elliptic Hypergeometric Functions
A new expansion for integral powers of the hypergeometric function corresponding to a special case of the incomplete beta function is summarized, and consequences, including two new sums involving digamma (psi) functions are presented.
Closed-form expressions for all matrix elements required for variational calculation of the electronic structure of periodic solids have been derived using a basis of explicitly correlated Gaussians (ECGs). Periodic basis functions are…
The purpose of this article is to demonstrate that i) the framework of elliptic hypergeometric integrals (EHIs) can be extended by input from supersymmetric gauge theory, and ii) analyzing the hyperbolic limit of the EHIs in the extended…
Fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients were constructed recently. These fundamental solutions are directly connected with multiple Lauricella hypergeometric function and…
We consider the generating function of the algebraic area of lattice walks, evaluated at a root of unity, and its relation to the Hofstadter model. In particular, we obtain an expression for the generating function of the n-th moments of…
The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients. These fundamental solutions are directly connected with multiple…
We study the problem of counting lattice points of a polytope that are weighted by an Ehrhart quasi-polynomial of a family of parametric polytopes. As applications one can compute integrals and maximum values of such quasi-polynomials, as…
We show how certain hypergeometric functions play an important role in finding fundamental solutions for a generalized Tricomi operator.
The aim of this paper is to give, using some contiguous relations, the asymptotic behaviour of some linear combination of two symmetric contiguous hypergeometric functions, under some conditions of their parameters.
In this paper, we first introduce certain forms of extended incomplete Pochhammer symbols which are then used to define families of extended incomplete generalized hypergeometric functions. For these functions, we investigate various…
We introduce several new identities combining basic hypergeometric sums and integrals. Such identities appear in the context of superconformal index computations for three-dimensional supersymmetric dual theories. We give both analytic…
Gauss-Hermite and Gauss-Laguerre ("shapelet") decompositions of images have become important tools in galaxy modeling, particularly for the purpose of extracting ellipticity and morphological information from astronomical data. However, the…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
The purpose of this article is to give an interpretation of real projective structures and associated cohomology classes in terms of connections, sections, etc. satisfying elliptic partial differential equations in the spirit of Hodge…
We introduce and investigate a class of $\mathfrak{gl}_{M+1}$ partition functions which is an extension of the one introduced by Foda-Manabe. We characterize the partition functions by a nested version of Izergin-Korepin analysis, and…
The asymptotic behaviour of partial sums of generalized hypergeometric series of unit argument is investigated.
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.…
We introduce new p-adic convergent functions, which we call the p-adic hypergeometric functions of logarithmic type. The first main result is to prove the congruence relations that are similar to Dwork's. The second main result is that the…
Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these limits, which arose in work of Wigner on the energy of static…
We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on…