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On Asymptotic Expansions of Generalized Stieltjes Functions

On Asymptotic Expansions of Generalized Stieltjes Functions We characterize the generalized Stieltjes functions corresponding to measures on the positive real axis having moments of all orders in terms of monotonicity properties of the remainders in asymptotic expansions of these functions. A special case furnishes a half line analogue of a classical theorem of Hamburger and Nevanlinna about asymptotic expansions of Cauchy transforms of measures having moments of all orders. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

On Asymptotic Expansions of Generalized Stieltjes Functions

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Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-014-0094-7
Publisher site
See Article on Publisher Site

Abstract

We characterize the generalized Stieltjes functions corresponding to measures on the positive real axis having moments of all orders in terms of monotonicity properties of the remainders in asymptotic expansions of these functions. A special case furnishes a half line analogue of a classical theorem of Hamburger and Nevanlinna about asymptotic expansions of Cauchy transforms of measures having moments of all orders.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Oct 22, 2014

References