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The paper focuses on an approximation of the first passage time probabilitydensity function of a Feller stochastic process by using cumulants and aLaguerre-Gamma polynomial approximation. The feasibility of the method relieson closed form formulae for cumulants and moments recovered from the Laplacetransform of the probability density function and using the algebra of formalpower series. To improve the approximation, sufficient conditions on cumulantsare stated. The resulting procedure is made easier to implement by the symboliccalculus and a rational choice of the polynomial degree depending on skewness,kurtosis and hyperskewness. Some case-studies coming from neuronal andfinancial fields show the goodness of the approximation even for a low numberof terms. Open problems are addressed at the end of the paper.

A cumulant approach for the first-passage-time problem of the Feller square-root process