On generating functions of hausdorff moment sequences

Journal Article (Journal Article)

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).

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Pego, RL

Published Date

  • January 1, 2016

Published In

Volume / Issue

  • 368 / 12

Start / End Page

  • 8499 - 8518

International Standard Serial Number (ISSN)

  • 0002-9947

Digital Object Identifier (DOI)

  • 10.1090/tran/6618

Citation Source

  • Scopus