ON GENERATING FUNCTIONS OF HAUSDORFF MOMENT SEQUENCES

The class of generating functions for completely monotone se- quences (moments of finite positive measures on (0, 1)) has an elegant char- acterization 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 r pn+r pn+r

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