One-parameter orthogonality relations for basic hypergeometric series

DOI10.1016/S0019-3577(03)90055-3zbMath1046.33011arXivmath/0305385MaRDI QIDQ1432902

H. T. Koelink

Publication date: 22 June 2004

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0305385

zbMATH Keywords

spectral analysisorthogonality relationsbasic hypergeometric serieshypergeometric \(q\)-difference operator

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (1)

Quantum groups, non-commutative \(AdS_2\), and chords in the double-scaled SYK model

Cites Work

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• Diagonalization of certain integral operators
• Transmutation kernels for the little \(q\)-Jacobi function transform.
• Fourier transforms on the quantum \(\text{SU}(1,1)\) group. (With an appendix by Mizan Rahman).
• An introduction to basic Fourier series
• The big \(q\)-Jacobi function transform
• Eigenfunction expansion associated with the Casimir operator on the quantum group \(SU_ q(1,1)\)
• Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. III: Associated continuous dual \(q\)-Hahn polynomials
• q-Integral and Moment Representations for q-Orthogonal Polynomials
• Spectral Theory of Jacobi Matrices in $l^2 (\mathbb{Z})$ and the $su(1,1)$ Lie Algebra
• Bilateral Birth and Death Processes

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