Multilateral Summation Theorems for Ordinary and Basic Hypergeometric Series in $U(n)$.
From MaRDI portal
Publication:3762626
DOI10.1137/0518114zbMath0624.33012OpenAlexW2009207359MaRDI QIDQ3762626
Publication date: 1987
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0518114
Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Classical hypergeometric functions, ({}_2F_1) (33C05)
Related Items
Quantum groups: A review, General multi-sum transformations and some implications, Nonterminating q-Whipple Transformations for Basic Hypergeometric Series in U(n), Inversions of integral operators and elliptic beta integrals on root systems, New transformations for elliptic hypergeometric series on the root system \(A_n\), Generalized bibasic hypergeometric series and their \(U(n)\) extensions, On the equivalence of two fundamental theta identities, On certain multiple Bailey, Rogers and Dougall type summation formulas, Connection formula for the Jackson integral of type \(A_n\) and elliptic Lagrange interpolation, A bilateral extension of the $q$-Selberg integral, Karlsson--Minton type hypergeometric functions on the root system \(C_{n}\), Trigonometric identities: from Hermite via Meijer, Nørlund, and Braaksma to Chu and Johnson and beyond, Mellin-Barnes integrals related to the Lie algebra \(u(N)\), New multiple \(_{6} \psi _{6}\) summation formulas and related conjectures, A new \(A_n\) extension of Ramanujan's \(_1\psi_1\) summation with applications to multilateral \(A_n\) series., A new class of symmetric polynomials defined in terms of tableaux, Elliptic hypergeometric series on root systems., Multidimensional matrix inversions and elliptic hypergeometric series on root systems, The \(q\)-Dixon-Anderson integral and multi-dimensional \(_1\psi_1\) summations, Multilateral inversion of \(A_{r}\), \(C_{r}\), and \(D_{r}\) basic hypergeometric series, Classical partition functions and the \(U(n+1)\) Rogers-Selberg identity, Harmonic analysis on the infinite-dimensional unitary group, Generalizations of Milne’s U(n + 1) q-Chu-Vandermonde summation, Partial fraction decompositions and trigonometric sum identities, On Warnaar's elliptic matrix inversion and Karlsson--Minton-type elliptic hypergeometric series, A new multivariable \(_{6 } \psi _{6 }\) summation formula, Nonsymmetric interpolation Macdonald polynomials and \({\mathfrak {gl}}_n\) basic hypergeometric series, Multivariable Wilson polynomials, The factorial Schur function