Related papers: Inversions of integral operators and elliptic beta…
A general method for analytic inversion of geometric integral transforms is proposed
We derive new reduction formulas for the incomplete beta function and the Lerch transcendent in terms of elementary functions. As an application, we calculate some new integrals. Also, we use these reduction formulas to test the performance…
We present an elliptic version of Selberg's integral formula.
The aim of this research paper is to demonstrate how one can obtain eleven new and interesting hypergeometric identities (in the form of a single result) from the old ones by mainly applying the well known beta integral method which was…
In this article we continue the work from arXiv:0902.0621. In that article Eric Rains and the present author considered the limits of the elliptic beta integral as p->0 while the parameters t_r have a p-dependence of the form…
Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and confluent hypergeometric functions. We systematically…
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
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…
In this article we give a new transformation between elliptic hypergeometric beta integrals, which gives rise to a Weyl group symmetry of type F_4. The transformation is a generalization of a series transformation discovered by Langer,…
We give an explicit Pieri formula for Macdonald polynomials attached to the root system C_n (with equal multiplicities). By inversion we obtain an explicit expansion for two-row Macdonald polynomials of type C.
We give a full list of known $\mathcal{N}=1$ supersymmetric quantum field theories related by the Seiberg electric-magnetic duality conjectures for $SU(N), SP(2N)$ and $G_2$ gauge groups. Many of the presented dualities are new, not…
The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…
We use the orientation underlying the Hirzebruch genus of level three to map the beta family at the prime p=2 into the ring of divided congruences. This procedure, which may be thought of as the elliptic greek letter beta construction,…
Matrix transformations in terms of triangular matrices is the easiest method of evaluating matrix-variate gamma and beta integrals in the real and complex cases. Here we give several procedures of explicit evaluation of gamma and beta…
Several methods of evaluation are presented for a family of Selberg-like integrals that arose in the computation of the algebraic-geometric degrees of a family of multiplicity-free nilpotent K_C-orbits. First, adapting the technique of…
We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
We develop a systematic and fully explicit approach to the evaluation of binomial sums involving reciprocals of binomial coefficients based on Beta integral techniques. Starting from a simple integral representation, we provide a derivation…
This work derives an application from the identities of arXiv:hep-th/0602028 in order to invert four point functions in defect conformal field theories. For this, a recursion relation is established and the O(N) model with a line defect is…
We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two form in essence an annotated table of the main evaluation and transformation formulas for elliptic…