The symmetric Meixner-Pollaczek polynomials with real parameter |
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Authors: | Tsehaye K. Araaya |
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Affiliation: | Department of Mathematics, Uppsala University 751 06 Uppsala, Box 480, Uppsala, Sweden |
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Abstract: | The Symmetric Meixner-Pollaczek polynomials for λ>0 are well-studied polynomials. These are polynomials orthogonal on the real line with respect to a continuous, positive real measure. For λ?0, are also polynomials, however they are not orthogonal on the real line with respect to any real measure. This paper defines a non-standard inner product with respect to which the polynomials for λ?0, become orthogonal polynomials. It examines the major properties of the polynomials, for λ>0 which are also shared by the polynomials, for λ?0. |
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Keywords: | Meixner-Pollaczek polynomial Orthogonal polynomial Polynomial operator Non-standard inner product |
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