  The paper focuses on an approximation of the first passage time probability
density function of a Feller stochastic process by using cumulants and a
Laguerre-Gamma polynomial approximation. The feasibility of the method relies
on closed form formulae for cumulants and moments recovered from the Laplace
transform of the probability density function and using the algebra of formal
power series. To improve the approximation, sufficient conditions on cumulants
are stated. The resulting procedure is made easier to implement by the symbolic
calculus and a rational choice of the polynomial degree depending on skewness,
kurtosis and hyperskewness. Some case-studies coming from neuronal and
financial fields show the goodness of the approximation even for a low number
of terms. Open problems are addressed at the end of the paper.
