We derive a Laguerre expansion for the inverse Laplace transform, based on the estimation problem in the gamma distribution. This procedure is used to obtain the density and distribution functions of a sum of positive weighted central chi-square variables as a series in Laguerre polynomials. The formulas so obtained will depend on certain parameters which adequately chosen will give some expressions already known in the literature and some new ones. Finally, we obtain bounds for the truncation error in the numerical approximations.
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Martínez et al. (2005) studied this question.
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