Math @ Duke

Publications [#320552] of JianGuo Liu
Papers Published
 Liu, JG; Pego, RL, On generating functions of hausdorff moment sequences,
Transactions of the American Mathematical Society, vol. 368 no. 12
(January, 2016),
pp. 84998518, American Mathematical Society (AMS) [doi]
(last updated on 2019/06/19)
Abstract: © 2016 American Mathematical Society. The class of generating functions for completely monotone sequences (moments of finite positive measures on [0, 1]) has an elegant characterization as the class of Pick functions analytic and positive on (−∞, 1). We establish this and another such characterization and develop a variety of consequences. In particular, we characterize generating functions for moments of convex and concave probability distribution functions on [0, 1]. Also we provide a simple analytic proof that for any real p and r with p > 0, the FussCatalan or Raney numbers (Formula Presented) are the moments of a probability distribution on some interval [0, τ] if and only if p ≥ 1 and p ≥ r ≥ 0. The same statement holds for the binomial coefficients (Formula Presented).


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