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).
 Andrews, G. E.Askey, R.Roy, R.1999Special FunctionsCambridge Univ. Press.
Andrews, G. E.Askey, R.Roy, R.1999Special FunctionsCambridge Univ. Press.)| false