An expansion theorem concerning Wilson functions and polynomials |
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Authors: | András Biró |
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Institution: | 1.A. Rényi Institute of Mathematics,Hungarian Academy of Sciences,Budapest,Hungary |
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Abstract: | We prove that a relatively general even function f(x) (satisfying a vanishing condition, and also some analyticity and growth conditions) on the real line can be expanded in
terms of a certain function series closely related to the Wilson functions introduced by Groenevelt in 2003. The coefficients
in the expansion of f will be inner products in a suitable Hilbert space of f and some polynomials closely related to Wilson polynomials (these are well-known hypergeometric orthogonal polynomials). |
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