Abstract
Tricomi’s method for computing a set of inverse Laplace transforms in terms of Laguerre polynomials is revisited. By using the more recent results about the inversion and the connection coefficients for the series of orthogonal polynomials, we find the possibility to extend the Tricomi method to more general series expansions. Some examples showing the effectiveness of the considered procedure are shown.
Highlights
In three notes presented to the Accademia dei Lincei in 1935 [1,2], Francesco G
As it is possible to transform the expansions in Laguerre polynomials, by using the inversion or the connection coefficients, into different expansions in terms of other polynomial sets, as it is shown in many articles [8,9,10,11], the above considerations suggest that we extend the Tricomi method in order to find different Laplace function pairs
We first apply the inversion coefficients in order to find the Laplace transform corresponding to a given power series, we apply the same methodology to the series of orthogonal polynomials
Summary
In three notes presented to the Accademia dei Lincei in 1935 [1,2], Francesco G. As it is possible to transform the expansions in Laguerre polynomials, by using the inversion or the connection coefficients, into different expansions in terms of other polynomial sets, as it is shown in many articles [8,9,10,11], the above considerations suggest that we extend the Tricomi method in order to find different Laplace function pairs. This is done even on the basis of preceding results in [12] and the connection of the Laplace transform with orthogonal polynomials, reported in [13]. We first apply the inversion coefficients in order to find the Laplace transform corresponding to a given power series, we apply the same methodology to the series of orthogonal polynomials
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