Related papers: Basic hypergeometry of supersymmetric dualities
The primitive elements of the supersymmetry algebra cohomology as defined in a previous paper are computed for standard supersymmetry algebras in four and five dimensions, for all signatures of the metric and any number of supersymmetries.
We give a simple unified proof for all existing rational hypergeometric Ramanujan identities for $1/\pi$, and give a complete survey (without proof) of several generalizations: rational hypergeometric identities for $1/\pi^c$, Taylor…
We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal…
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…
We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general cubic algebra and we present specific…
A hypergeometric identity equating a triple sum to a single sum, originally found by Gelfand, Graev and Retakh [Russian Math. Surveys 47 (1992), 1-88] by using systems of differential equations, is given hypergeometric proofs. As a bonus,…
We prove a summation formula for a bilateral series whose terms are products of two basic hypergeometric functions. In special cases, series of this type arise as matrix elements of quantum group representations.
We review the calculation and properties of the supersymmetric index for four dimensional N=1 theories, illustrating its physical significance in several examples.
We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
We obtain new trigonometric identities, which are some product-to-sum type formulas for the higher derivative of the cotangent and cosecant functions. Further, from specializations of our formulas, we derive not only various known…
In this short note, we establish some identities containing sums of binomials with coefficients satisfying third order linear recursive relations. As a result and in particular, we obtain general forms of earlier identities involving…
The interaction between combinatorics and algebraic and differential geometry is very strong. While researching a problem of Hessian topology, we came across a series of identities of binomial coefficients, which are useful for proving a…
We introduce superequivalence and superuniform spaces.
Hidden symmetries, described by higher order in momenta integrals of motion that generate nonlinear algebras, are explored at the level of classical and quantum mechanics in a variety of physical systems related to conformal and…
We prove a pair of transformation formulas for multivariate elliptic hypergeometric sum/integrals associated to the $A_n$ and $BC_n$ root systems, generalising the formulas previously obtained by Rains. The sum/integrals are expressed in…
In a Hom-superalgebra, a super-identity equivalent to the Hom-Malcev super-identity is found.
We define and study the structure of SUSY Lie conformal and vertex algebras. This leads to effective rules for computations with superfields.