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A right inverse of the Askey-Wilson operator

B. Malcolm Brown·Mourad E. H. Ismail
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Abstract

We establish an integral representation of a right inverse of the Askey-Wilson finite difference operator on $L^2$ with weight $(1-x^2)^{-1/2}$. The kernel of this integral operator is $\vartheta'_4/\vartheta_4$ and is the Riemann mapping function that maps the open unit disc conformally onto the interior of an ellipse.

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B. Malcolm Brown, Mourad E. H. Ismail. 1993-10-05. A right inverse of the Askey-Wilson operator. https://arxiv.org/abs/math/9310219

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