Nonterminating q-Whipple Transformations for Basic Hypergeometric Series in U(n)

DOI10.1007/978-1-4614-0028-8_12zbMath1245.33018OpenAlexW34166650MaRDI QIDQ2897236

John W. Newcomb, Stephen C. Milne

Publication date: 10 July 2012

Published in: Partitions, q-Series, and Modular Forms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4614-0028-8_12

zbMATH Keywords

_{10}\boldsymbol{\phi}_{9}\) transformation formulasmultiple basic hypergeometric series associated to root systemsU\((n + 1)\U\((n + 1)\) nonterminating \(q\)-Saalschütz transformationsU\((n + 1)\) nonterminating \(q\)-Whipple transformations

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) (q)-calculus and related topics (05A30) Other basic hypergeometric functions and integrals in several variables (33D70)

Related Items (3)

Expansion formulas for multiple basic hypergeometric series over root systems ⋮ \(U(n)\) very-well-poised \(_{10}\phi_ 9\) transformations ⋮ A nonterminating \(_8\phi_7\) summation for the root system \(C_r\).

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
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multivariate basic hypergeometric series associated to root systems of type \(A_{m}\)
• Multilateral inversion of \(A_{r}\), \(C_{r}\), and \(D_{r}\) basic hypergeometric series
• The \(C_ \ell\) Bailey transform and Bailey lemma
• Reduction formulas for Karlsson-Minton-type hypergeometric functions
• Multiple analogues of binomial coefficients and families of related special numbers
• Nonsymmetric interpolation Macdonald polynomials and \({\mathfrak {gl}}_n\) basic hypergeometric series
• \(BC_n\)-symmetric abelian functions
• Basic hypergeometric functions as limits of elliptic hypergeometric functions
• Transformations of elliptic hypergeometric integrals
• Limits of elliptic hypergeometric integrals
• A q-analog of the \(_5F_4(1)\) summation theorem for hypergeometric series well-poised in \(SU(n)\)
• An elementary proof of the Macdonald identities for \(A_{\ell}^{(1)}\)
• A q-analog of hypergeometric series well-poised in SU(n) and invariant G-functions
• A \(U(n)\) generalization of Ramanujan's \(_1\Psi_1\) summation
• Basic hypergeometric series very well-poised in U(n)
• A q-analog of the Gauss summation theorem for hypergeometric series in U(n)
• Multidimensional matrix inversions and \(A_r\) and \(D_r\) basic hypergeometric series
• Classical partition functions and the \(U(n+1)\) Rogers-Selberg identity
• \(C_n\) and \(D_n\) very-well-poised \(_{10}\varphi_9\) transformations
• A new multidimensional matrix inverse with applications to multiple \(q\)-series
• \(D_n\) basic hypergeometric series
• A \(q\)-analog of a Whipple's transformation for hypergeometric series in \(U(n)\)
• Balanced \(_ 3\phi_ 2\) summation theorems for \(U(n)\) basic hypergeometric series
• Generalized bibasic hypergeometric series and their \(U(n)\) extensions
• On certain multiple Bailey, Rogers and Dougall type summation formulas
• A nonterminating \(_8\phi_7\) summation for the root system \(C_r\).
• A new \(A_n\) extension of Ramanujan's \(_1\psi_1\) summation with applications to multilateral \(A_n\) series.
• 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
• Modular hypergeometric residue sums of elliptic Selberg integrals
• Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions
• A product formula for Jackson integral associated with the root system \(F_4\)
• Summation and transformation formulas for elliptic hypergeometric series.
• Some basic extensions of Gustafson-Rakha's multivariate basic hypergeometric series
• Euler transformation formula for multiple basic hypergeometric series of type \(A\) and some applications
• 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
• Some new applications of matrix inversions in \(A_r\)
• Multidimensional matrix inversions and elliptic hypergeometric series on root systems
• Generalized hypergeometric functions with applications in statistics and physical sciences
• Inversion of the Pieri formula for Macdonald polynomials
• Dedekind's η-function and Rogers-Ramanujan identities
• An elliptic $BC_n$ Bailey Lemma, multiple Rogers–Ramanujan identities and Euler’s Pentagonal Number Theorems
• Multilateral basic hypergeometric summation identities and hyperoctahedral group symmetries
• Multilateral Summation Theorems for Ordinary and Basic Hypergeometric Series in $U(n)$.
• On Hypergeometric Series Well-Poised in $SU(n)$
• A Summation Theorem for Hypergeometric Series Very-Well-Poised on $G_2 $
• The $C_\ell $ Rogers–Selberg Identity
• The major counting of nonintersecting lattice paths and generating functions for tableaux
• New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function
• Cylindric Partitions
• An elliptic Macdonald-Morris conjecture and multiple modular hypergeometric sums
• \(q\)-beta integrals and multivariate basic hypergeometric series associated to root systems of type \(A_m\)

This page was built for publication: Nonterminating q-Whipple Transformations for Basic Hypergeometric Series in U(n)