Integrals of the Laplace's type can be evaluated asymptotically by use of Taylor series expansion about the origin and integrating the resulting series term by term. Let the integral be given by:

f(p} = J e -pt F(t) dt 0

Expanding F(t) in a Taylor series about t = 0, F(t) can be written as a sum, i.e.: oo F(n)(O)

where f(n) is the nth derivative. Integrating each term in eq. (9.1) results in an asymptotic series for f(p ):

and where f(x) is the Gamma function, see Appendix B 1.