21. Hsu was an expert in manipulating characteristic functions . 22. He was an expert in operating matrix, manipulating characteristic functions and integral transformation. 23. Some are based on summations of random variables and others on properties of characteristic functions . 24. The characteristic function in probability theory. 25. The characteristic function is listed incorrectly in many standard references ( e . g ., is 26. The characteristic function of the Dirichlet distribution is a confluent form of the Lauricella hypergeometric series. 27. The latter was obtained by introducing an equivalent but tractable form of the Heston characteristic function . 28. Since the Holtsmark distribution has \ alpha = 3 / 2, its characteristic function is: 29. When \ beta is zero the distribution is symmetric, and the characteristic function reduces to: 30. The geometric stable characteristic function can be expressed in terms of a stable characteristic function as:
