The Laguerre transform in practice
Keenan, Colin N.
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An attempt was made to find a method for generating a useful analytic expression for the Laplace or inverse Laplace transform of a given set of data. The method attempted involved first fitting the data to Laguerre functions. In the process, computer algorithms for doing a Laguerre transform were found. However, the analytic expression for the Laplace transform that results from this method is not directly useful because it is usually hundreds of terms long. The Laguerre transform routines are comprehensive, including methods for estimating the number of Laguerre functions needed for the transform to be representative of the original data. The transform is considered representative of the original data if the inverse transform returns the original data within a small x2- Fourier transform methods are used in this estimate. The methods developed here for the Laguerre transform can be generalized to transforms using other recursively generated sets of orthogonal functions.