### Actuarial values calculated using the incomplete Gamma function

G. Mingari Scarpello, D. Ritelli & D. Spelta
The complete expectation-of-life for a person and the actuarial present value of continuous life annuities are defined by integrals. In all of them at least one of the factors is a survival function value ratio. If de Moivre’s law of mortality is chosen, such integrals can easily be evaluated; but if the Makeham survival function is adopted, they are used to be calculated numerically. For the above actuarial figures, closed form integrations are hereafter provided...