Heine's method and \(A_{n}\) to \(A_{m}\) transformation formulas

DOI10.1007/s11139-018-0062-3zbMath1408.33035arXiv1705.10095OpenAlexW2900168923WikidataQ64894393 ScholiaQ64894393MaRDI QIDQ1733374

Gaurav Bhatnagar

Publication date: 21 March 2019

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.10095

zbMATH Keywords

\(A_n\) basic hypergeometric series\(q\)-Lauricella functions\(U(n+1)\) basicbibasic Heine transformation formulaRamanujan's \(_2\phi _1\) transformations

Mathematics Subject Classification ID

Basic hypergeometric functions associated with root systems (33D67) Bibasic functions and multiple bases (33D65)

Related Items (1)

Stokes phenomena in 3d \(\mathcal{N} = 2 \) \(\mathrm{SQED}_2\) and \(\mathbb{CP}^1\) models

Cites Work

• Certain \(q\)-series identities
• The \({\mathfrak{sl}}_3\) Selberg integral
• \(C_n\) and \(D_n\) very-well-poised \(_{10}\varphi_9\) transformations
• Balanced \(_ 3\phi_ 2\) summation theorems for \(U(n)\) basic hypergeometric series
• Generalized bibasic hypergeometric series and their \(U(n)\) extensions
• Elliptic hypergeometric series on root systems.
• Multiple elliptic hypergeometric series. An approach from the Cauchy determinant
• Transformation formulas for multivariable basic hypergeometric series
• A bibasic Heine transformation formula and Ramanujan's \(_2\phi_1\) transformations
• Elliptic well-poised Bailey transforms and lemmas on root systems
• 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
• Heine transformations for a new kind of basic hypergeometric series in \(U(n)\)
• Multiple Generalizations of q-Series Identities and Related Formulas
• $q$-Selberg integrals and Macdonald polynomials
• Ramanujan's Lost Notebook
• ON BASIC HYPERGEOMETRIC SERIES, MOCK THETA FUNCTIONS, AND PARTITIONS (I)
• Summations and Transformations for Basic Appell Series
• Cylindric Partitions
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