The lognormal characteristic function
PHILIP HOLGATE · Communication in Statistics- Theory and Methods · 1989
A number of different ways are examined of representing the characteristic function φ(t) of the lognormal distribution, which cannot be expanded in a Taylor series based on the moments. In §2 the use of a finite Taylor series is examined. A method of summing the divergent formal expansion is discussed in §3. In §4 the fact that φ(t) is a boundary analytic function is exploited. Asymptotic approximation of the integral defining φ(t) is studied in §5. Each approach produces some interesting information about the distribution.