Summation and transformation formulas for elliptic hypergeometric series.

DOI10.1007/s00365-002-0501-6zbMath1040.33013arXivmath/0001006OpenAlexW2106488453WikidataQ64385599 ScholiaQ64385599MaRDI QIDQ1862754

S. Ole Warnaar

Publication date: 2002

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0001006

zbMATH Keywords

elliptic functionselliptic hypergeomeytric series.

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic hypergeometric functions associated with root systems (33D67) Elliptic functions and integrals (33E05) Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable (33D50)

Related Items

Introduction to the theory of elliptic hypergeometric integrals, Elliptic hypergeometric summations by Taylor series expansion and interpolation, Nonterminating q-Whipple Transformations for Basic Hypergeometric Series in U(n), Gustafson-Rakha-type elliptic hypergeometric series, Higher order deformed elliptic Ruijsenaars operators, Zeros of the i.i.d. Gaussian Laurent series on an annulus: weighted Szegő kernels and permanental-determinantal point processes, The determinant of an elliptic sylvesteresque matrix, \(BC_n\)-symmetric abelian functions, \(q\)-hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theorem, Inversions of integral operators and elliptic beta integrals on root systems, The \((f,g)\)-inversion formula and its applications: the \((f,g)\)-summation formula, Strange evaluations of Fox–Wright function, New transformations for elliptic hypergeometric series on the root system \(A_n\), Summation formulae for elliptic hypergeometric series, ABEL'S METHOD ON SUMMATION BY PARTS FOR ELLIPTIC HYPERGEOMETRIC SERIES, A novel extension of the Lagrange-Bürmann expansion formula, Elliptic enumeration of nonintersecting lattice paths, \(q\)-distributions on boxed plane partitions, Partial isometries, duality, and determinantal point processes, Quartic theta hypergeometric series, A $4n$-Point Elliptic Interpolation Formula and its Applications, Symmetry of terminating basic hypergeometric series representations of the Askey-Wilson polynomials, A noncommutative weight-dependent generalization of the binomial theorem, Selberg integrals, Askey-Wilson polynomials and lozenge tilings of a hexagon with a triangular hole, Shifted versions of the Bailey and well-poised Bailey lemmas, Lattice paths and negatively indexed weight-dependent binomial coefficients, A multilateral Bailey lemma and multiple Andrews-Gordon identities, Elliptic determinantal processes and elliptic Dyson models, Two matrix inversions associated with the Hagen-Rothe formula, their \(q\)-analogues and applications, New multiple \(_{6} \psi _{6}\) summation formulas and related conjectures, Elliptic Littlewood identities, A nonterminating \(_8\phi_7\) summation for the root system \(C_r\)., Elliptic beta integrals and modular hypergeometric sums: An overview., Multiple gamma function, its \(q\)- and elliptic analogue., Wronskian type determinants of orthogonal polynomials, Selberg type formulas and constant term identities, Elliptic hypergeometric series on root systems., An elliptic $BC_n$ Bailey Lemma, multiple Rogers–Ramanujan identities and Euler’s Pentagonal Number Theorems, Macdonald denominators for affine root systems, orthogonal theta functions, and elliptic determinantal point processes, Multidimensional matrix inversions and elliptic hypergeometric series on root systems, Multiple elliptic hypergeometric series. An approach from the Cauchy determinant, Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations, Extensions of the well-poised and elliptic well-poised Bailey lemma, Best polynomial approximation on the triangle, Elliptic free-fermion model with OS boundary and elliptic Pfaffians, Abel's method on summation by parts and theta hypergeometric series, Elliptic determinantal process of type A, Elliptic rook and file numbers, Elliptic well-poised Bailey transforms and lemmas on root systems, Combinatorial formulas for certain sequences of multiple numbers, Elliptically distributed lozenge tilings of a hexagon, Derivation of a \(BC_n\) elliptic summation formula via the fundamental invariants, Positivity preserving transformations for 𝑞-binomial coefficients, Two-dimensional elliptic determinantal point processes and related systems, A \(U(n + 1)\) Bailey lattice, Transformations of elliptic hypergeometric integrals, Multiple analogues of binomial coefficients and families of related special numbers, On Warnaar's elliptic matrix inversion and Karlsson--Minton-type elliptic hypergeometric series, Theta hypergeometric integrals, An elliptic hypergeometric function approach to branching rules, Excursion processes associated with elliptic combinatorics, Duality transformation formulas for multiple elliptic hypergeometric series of type \(BC\), Discrete analogues of Macdonald-Mehta integrals, Telescoping method, summation formulas, and inversion pairs, The \(C_n\) WP-Bailey chain, Elliptic Bessel processes and elliptic Dyson models realized as temporally inhomogeneous processes, Bounded Littlewood identities, Advanced determinant calculus: a complement, On a generalized Weierstrass theta identity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Another family of q-Lagrange inversion formulas
• Multidimensional matrix inversions and \(A_r\) and \(D_r\) basic hypergeometric series
• Determinants in plane partition enumeration
• \(C_n\) and \(D_n\) very-well-poised \(_{10}\varphi_9\) transformations
• Advanced determinant calculus
• A \(q\)-analog of a Whipple's transformation for hypergeometric series in \(U(n)\)
• Generalized bibasic hypergeometric series and their \(U(n)\) extensions
• On certain multiple Bailey, Rogers and Dougall type summation formulas
• A characterization of inverse relations.
• Consequences of the \(A_ l\) and \(C_ l\) Bailey transform and Bailey lemma
• \(U(n)\) very-well-poised \(_{10}\phi_ 9\) transformations
• Summation theorems for multidimensional basic hypergeometric series by determinant evaluations
• An Indefinite Bibasic Summation Formula and Some Quadratic, Cubic and Quartic Summation and Transformation Formulas
• Applications of q-Lagrange Inversion to Basic Hypergeometric Series
• Summation, Transformation, and Expansion Formulas for Bibasic Series
• Orthogonal Functions from Gram Determinants
• An $SU(n)$q-Beta Integral Transformation and Multiple Hypergeometric Series Identities
• First order analytic difference equations and integrable quantum systems
• The major counting of nonintersecting lattice paths and generating functions for tableaux
• A new matrix inverse
• Some Quadratic and Cubic Summation Formulas for Basic Hypergeometric Series
• The elliptic gamma function and \(\text{SL}(3,\mathbb Z)\ltimes\mathbb Z^3\).
• Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. II: Equivalence to a generalized ice-type lattice model.