A \(U(n)\) generalization of Ramanujan's \(_1\Psi_1\) summation

DOI10.1016/0022-247X(86)90308-2zbMath0594.33008MaRDI QIDQ1076862

Stephen C. Milne

Publication date: 1986

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

elliptic functionsMacdonald identitiesq-hypergeometric series

Mathematics Subject Classification ID

Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05)

Related Items (10)

Basic hypergeometric series very well-poised in U(n) ⋮ Nonterminating q-Whipple Transformations for Basic Hypergeometric Series in U(n) ⋮ A q-analog of the Gauss summation theorem for hypergeometric series in U(n) ⋮ Connection formula for the Jackson integral of type \(A_n\) and elliptic Lagrange interpolation ⋮ Multivariable biorthogonal continuous–discrete Wilson and Racah polynomials ⋮ A bilateral extension of the $q$-Selberg integral ⋮ A new \(A_n\) extension of Ramanujan's \(_1\psi_1\) summation with applications to multilateral \(A_n\) series. ⋮ The \(q\)-Dixon-Anderson integral and multi-dimensional \(_1\psi_1\) summations ⋮ Classical partition functions and the \(U(n+1)\) Rogers-Selberg identity ⋮ Multivariable Wilson polynomials

Cites Work

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• 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
• Lie algebraic approaches to classical partition identities
• A simple proof of Ramanujan's summation of the \(_1\Psi_1\)
• A multiple series transformation of the very well poised \(_{2k+4}\Phi_{2k+4}\)
• Affine root systems and Dedekind's \(\eta\)-function
• Missed opportunities
• Ramanujan's Extensions of the Gamma and Beta Functions
• Shorter Notes: A Simple Proof of Ramanujan's 1 Ψ 1 Sum
• The Very Well Poised 6 ψ 6
• On the Geometry of Numbers in Elementary Number Theory
• Shorter Notes: On Ramanujan's Summation of 1 ψ 1 (a; b; z)
• On a Transformation of Bilateral Series with Applications
• An elementary proof of p(11m+6)≡0 (mod 11)
• Beiträge zur Theorie der Heineschen Reihen. Die 24 Integrale der hypergeometrischen q‐Differenzengleichung. Das q‐Analogon der Laplace‐Transformation
• On Lerch's Transcendant and the Basic Bilateral Hypergeometric Series ₂ ψ₂

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