A right inverse of the Askey-Wilson operator

Mathematics – Classical Analysis and ODEs

Scientific paper

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Scientific paper

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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