Abstract
By use of a special case of Slater’s q-beta integral evaluation formula, we determine orthogonality relations for the Al-Salam–Carlitz polynomials of type II with respect to a family of measures supported on a discrete subset of R. From spectral analysis of the corresponding second-order q-difference operator we obtain an infinite set of functions that complement the Al-Salam–Carlitz II polynomials to an orthogonal basis of the associated L2-space.
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