41. There is also a relationship between the stable distribution characteristic function and the geometric stable distribution characteristic function . 42. The rational approximation software RARL2 is used to approximate the discrete time rational characteristic function of the density. 43. There are particularly simple results for the characteristic functions of distributions defined by the weighted sums of random variables. 44. This framework may be viewed as a generalization of the characteristic function under specific choices of the kernel function. 45. It follows that the moments are simply equal to the characteristic function of the unwrapped distribution for integer arguments: 46. The class contains the density functions of all distributions that have characteristic functions that are strictly proper rational functions. 47. The proper use of tables of the characteristic function also rely on the " less than or equal " formulation. 48. In consequence, the characteristic function of the log-normal distribution cannot be represented as an infinite convergent series. 49. The moment-generating function of a real-valued distribution does not always exist, unlike the characteristic function . 50. Clearly the approach via ( 1.1 ) and ( 3.1 ) does not involve characteristic functions .
