Related papers: Basic hypergeometry of supersymmetric dualities
We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…
Identities involving finite sums of products of hypergeometric functions and their duals have been studied since 1930s. Recently Beukers and Jouhet have used an algebraic approach to derive a very general family of duality relations. In…
A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.
Four dimensional $\mathcal{N}=2$ Argyres-Douglas theories have been recently conjectured to be described by $\mathcal{N}=1$ Lagrangian theories. Such models, once reduced to 3d, should be mirror dual to Lagrangian $\mathcal{N}=4$ theories.…
We show that several terminating summation and transformation formulas for basic hypergeometric series can be proved in a straightforward way. Along the same line, new finite forms of Jacobi's triple product identity and Watson's quintuple…
We construct the Hodge dual for supermanifolds by means of the Grassmannian Fourier transform of superforms. In the case of supermanifolds it is known that the superforms are not sufficient to construct a consistent integration theory and…
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…
We obtain the lens integral pentagon identity for three-dimensional mirror dual theories in terms of hyperbolic hypergeometric functions via reduction of equality for $\mathcal N=2$ lens supersymmetric partition functions of a certain…
In 2015, Ebisu presented a new method for finding hypergeometric identities based on three-term relations for the ${}_{2} F_{1}$ hypergeometric series. By using this method, he derived almost all of the previously known hypergeometric…
Mathematical functions, which often appear in mathematical analysis, are referred to as special functions and have been studied over hundreds of years. Many books and dictionaries are available that describe their properties and serve as a…
We establish two binomial coefficient--generalized harmonic sum identities using the partial fraction decomposition method. These identities are a key ingredient in the proofs of numerous supercongruences. In particular, in other works of…
We consider field theory side of new multiple Seiberg dualities conjectured within superconformal index matching approach. We study the case of SU(2) supersymmetric QCD and find that the numerous conjectured duals are different faces of…
The partition functions of three-dimensional N=2 supersymmetric gauge theories on different manifolds can be expressed as q-hypergeometric integrals. By comparing the partition functions of three-dimensional mirror dual theories, one finds…
Recently Kashaev, Luo and Vartanov, using the reduction from a four-dimensional superconformal index to a three-dimensional partition function, found a pentagon identity for a special combination of hyperbolic Gamma functions. Following…
In this note, we shall provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence formulas.
Motivated by the work on hypergeometric summation theorems (recorded in the table III of Prudnikov et al. pp. 541-546), we have established some new summation theorems for Clausen's hypergeometric functions with unit argument in terms of…
The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to present the recent progress in this direction.
We prove an interesting identity for the sum of determinants, which is a generalization of the sum of a geometric progression. The proof is quite long and a number of other identities are proved along the way. Some of the more elementary…
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…
By systematically applying ten well-known and inequivalent two-part relations between hypergeometric sums 3F2(...|1) to the published database of all such sums, 62 new sums are obtained. The existing literature is summarized, and many…