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Optimal parametrization of truncated generalized Laguerre series

In this paper we address the problem of approximating functions on a semi-infinite interval by truncated series of orthonormal generalized Laguerre functions. The generalized Laguerre functions contain two parameters, namely a scale factor and an order of generalization. The rate of convergence of a generalized Laguerre series depends on the choice of these parameters. Results concerning the determination of the two parameters are presented.