A generalization of Selberg’s beta integral
From MaRDI portal
Publication:3035581
DOI10.1090/S0273-0979-1990-15852-5zbMath0693.33001MaRDI QIDQ3035581
Publication date: 1990
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Related Items
Macdonald’s constant term conjectures for exceptional root systems, A generalization of the Sears-Slater transformation and elliptic Lagrange interpolation of type \(BC_{n}\), Evaluation of the $BC_n$ elliptic Selberg integral via the fundamental invariants, Askey-Wilson type integrals associated with root systems, Rarefied elliptic hypergeometric functions, Geometric \(q\)-hypergeometric functions as a bridge between Yangians and quantum affine algebras, Inversions of integral operators and elliptic beta integrals on root systems, On certain multiple Bailey, Rogers and Dougall type summation formulas, Rational function certification of multisum/integral/“𝑞” identities, A bilateral extension of the $q$-Selberg integral, Superconformal indices of \({{\mathcal N}=4}\) SYM field theories, Vanishing integrals for Hall-Littlewood polynomials, Twisted strong Macdonald theorems and adjoint orbits, New multiple \(_{6} \psi _{6}\) summation formulas and related conjectures, The importance of the Selberg integral, Elliptic hypergeometric series on root systems., Integral representations of the Wilson polynomials and the continuous dual Hahn polynomials, BGG reciprocity for current algebras, The \(q\)-Dixon-Anderson integral and multi-dimensional \(_1\psi_1\) summations, Askey-Wilson polynomials by means of a \(q\)-Selberg type integral, Some limit transitions between BC type orthogonal polynomials interpreted on quantum complex Grassmannians, Symmetric and nonsymmetric Koornwinder polynomials in the \(q \to 0\) limit, Multivariate quadratic transformations and the interpolation kernel, Another proof of Gustafson's \(C_n\)-type summation formula via `elementary' symmetric polynomials, A proof of the two parameter \(q\)-cases of the Macdonald-Morris constant term root system conjecture for \(S(F_ 4)\) and \(S(F_ 4)^ \vee\) via Zeilberger's method, Identities in search of identity, Hyperbolic beta integrals, An algebraic approach to Macdonald–Koornwinder polynomials: Rodrigues-type formula and inner product identity, \(q\)-difference shift for a \(BC_{n}\)-type Jackson integral arising from `elementary' symmetric polynomials, A simple proof of an Aomoto-type extension of Askey's last conjectured Selberg \(q\)-integral, On $BC$ type basic hypergeometric orthogonal polynomials, An elliptic hypergeometric function approach to branching rules, Branching formula for Macdonald-Koornwinder polynomials, A determinant formula for a holonomic \(q\)-difference system associated with Jackson integrals of type \(BC_n\), A determinant formula associated with the elliptic hypergeometric integrals of type BC n, Multivariable Wilson polynomials and degenerate Hecke algebras, \(q\)-Selberg integrals and Koornwinder polynomials, Bounded Littlewood identities, A multidimensional generalization of the Barnes integral and the continuous Hahn polynomial, Properties of some families of hypergeometric orthogonal polynomials in several variables, A duality of MacDonald-Koornwinder polynomials and its application to integral representations, Unit circle elliptic beta integrals, An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities, A constant term identity featuring the ubiquitous (and mysterious) Andrews-Mills-Robbins-Rumsey numbers \(1, 2, 7, 42, 429, \dots\)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Some applications of hypergeometric shift operators
- A proof of Andrews' \(q\)-Dyson conjecture
- A proof of the two parameter \(q\)-cases of the Macdonald-Morris constant term root system conjecture for \(S(F_ 4)\) and \(S(F_ 4)^ \vee\) via Zeilberger's method
- The Poincaré series of a Coxeter group
- Tensor product spaces
- Affine root systems and Dedekind's \(\eta\)-function
- Statistical Theory of the Energy Levels of Complex Systems. I
- A Proof of the Macdonald–Morris Root System Conjecture for $F_4 $
- Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
- Another Conjectured q-Selberg Integral
- Jacobi Polynomials Associated with Selberg Integrals
- A Proof of the $G_2 $ Case of Macdonald’s Root System-Dyson Conjecture
- A Unified Approach to Macdonald’s Root-System Conjectures
- Proof of a Conjecture by Dyson in the Statistical Theory of Energy Levels
- Some Hypergeometric Orthogonal Polynomials
- A q-Beta Integral Associated with $BC_1 $
- Some q-Beta and Mellin-Barnes Integrals on Compact Lie Groups and Lie Algebras
- A proof of the 𝑞-Macdonald-Morris conjecture for 𝐵𝐶_{𝑛}
- Proof of a Conjecture by Dyson
