One-parameter orthogonality relations for basic hypergeometric series

Details One-parameter orthogonality relations for basic hypergeometric series One-parameter orthogonality relations for basic hypergeometric series

2003-05-27

arxiv.org/abs/math/0305385v1

Indagationes Mathematicae N.S. 14 (2003), 423-443

Mathematics

Classical Analysis and ODEs

18 pages, to appear in Indagationes Mathematicae

Scientific paper

The second order hypergeometric q-difference operator is studied for the value c=-q. For certain parameter regimes the corresponding recurrence relation can be related to a symmetric operator on the Hilbert space l^2(Z). The operator has deficiency indices (1,1) and we describe as explicitly as possible the spectral resolutions of the self-adjoint extensions. This gives rise to one-parameter orthogonality relations for sums of two 2\phi1-series. In particular, we find that the Ismail-Zhang q-analogue of the exponential function satisfies certain orthogonality relations analogous to the Fourier cosine transform.

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