Some Basic Lommel Polynomials |
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Authors: | H T Koelink |
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Institution: | Vakgroep Wiskunde, Universiteit van Amsterdam, Plantage Muidergracht 24, 10187 TV, Amsterdam, The Netherlandsf1 |
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Abstract: | The basic Lommel polynomials associated to the11q-Bessel function and the Jacksonq-Bessel functions are considered as orthogonal polynomials inqν, whereνis the order of the corresponding basic Bessel functions. The corresponding moment problems are both indeterminate and determinate depending on a parameter. Using techniques of Chihara and Maki we derive an explicit orthogonality measure, which is discrete and unbounded. For the indeterminate moment problem this measure is N-extremal. Some results on the zeros of the basic Bessel functions, both as functions of the order and of the argument are obtained. Precise asymptotic behaviour of the zeros of the11q-Bessel function is obtained. |
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