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