Publications [#320552] of Jian-Guo Liu

Papers Published

1. Liu, JG; Pego, RL, On generating functions of hausdorff moment sequences, Transactions of the American Mathematical Society, vol. 368 no. 12 (January, 2016), pp. 8499-8518, American Mathematical Society (AMS) [doi]
   (last updated on 2024/04/24)

   Abstract:
   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 Fuss-Catalan 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).