Related papers: Elliptic hypergeometric functions associated with …
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…
In this paper we treat certain elliptic and hyper-elliptic integrals in a unified way. We introduce a new basis of these integrals coming from certain basis ${\phi}_n(x)$ of polynomials and show that the transition matrix between this basis…
We briefly discuss the transcendental constants generated through the epsilon-expansion of generalized hypergeometric functions and their interrelation with the "sixth root of unity."
The parabolic trigonometric functions have recently been introduced as an intermediate step between circular and hyperbolic functions. They have been shown to be expressible in terms of irrational functions, linked to the solution of third…
The main purpose of this paper is to compute all irreducible spherical functions on $G=\SU(3)$ of arbitrary type $\delta\in \hat K$, where $K={\mathrm{S}}(\mathrm{U}(2)\times\mathrm{U}(1))\simeq\mathrm{U}(2)$. This is accomplished by…
Revisiting canonical integration of the classical solid near a uniform rotation, canonical action angle coordinates, hyperbolic and elliptic, are constructed in terms of various power series with coefficients which are polynomials in a…
Geometric variations of local systems are families of variations of Hodge structure; they typically correspond to fibrations of K\"{a}hler manifolds for which each fibre itself is fibred by codimension one K\"{a}hler manifolds. In this…
A double covering of the proper orthochronous Lorentz group is understood as a complexification of the special unimodular group of second order (a double covering of the 3-dimensional rotation group). In virtue of such an interpretation the…
Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in…
From the algebraic solution of $x^{n}-x+t=0$ for $n=2,3,4$ and the corresponding solution in terms of hypergeometric functions, we obtain a set of reduction formulas for hypergeometric functions. By differentiation and integration of these…
Hypergeometric functions of one and many variables play an important role in various branches of modern physics and mathematics. Often we have hypergeometric functions with indices linear dependent on a small parameter with respect to which…
In this paper we give a survey of elliptic theory for operators associated with diffeomorphisms of smooth manifolds. Such operators appear naturally in analysis, geometry and mathematical physics. We survey classical results as well as…
This is a review of ($q$-)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable theory, and to knot theory. We discuss both continuous and discrete orthogonal…
In this paper, we prove two structural theorems on the general Berndt-type integrals with the denominator having arbitrary positive degrees by contour integrations involving hyperbolic and trigonometric functions, and hyperbolic sums…
We obtain several determinant evaluations, related to affine root systems, which provide elliptic extensions of Weyl denominator formulas. Some of these are new, also in the polynomial special case, while others yield new proofs of the…
We derive ground state eigenfunctions and eigenvalues of various relativistic elliptic integrable models. The models we discuss appear in computations of superconformal indices of four-dimensional theories obtained by compactifying…
We construct the quantum double ramification hierarchy associated with the Gromov-Witten theory of elliptic curves. We use results of Oberdieck and Pixton on the intersection numbers of the double ramification cycle, the Gromov-Witten…
We evaluate several classes of high weight hypergeometric series via Gamma, polylogarithm and elliptic integrals, mainly through distribution relations.
A new type of sl_3 basic hypergeometric series based on Macdonald polynomials is introduced. Besides a pair of Macdonald polynomials attached to two different sets of variables, a key-ingredient in the sl_3 basic hypergeometric series is a…
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…