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Wall's continued-fraction characterization of Hausdorff moment sequences: A conceptual proof


Author: Alan D. Sokal
Journal: Proc. Amer. Math. Soc. 148 (2020), 2111-2116
MSC (2010): Primary 44A60; Secondary 05A15, 30B70, 30E05
DOI: https://doi.org/10.1090/proc/14884
Published electronically: January 29, 2020
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Abstract: I give an elementary proof of Wall's continued-fraction characterization of Hausdorff moment sequences.


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Alan D. Sokal
Affiliation: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom; and Department of Physics, New York University, 726 Broadway, New York, New York 10003
Email: sokal@math.ucl.ac.uk, sokal@nyu.edu

DOI: https://doi.org/10.1090/proc/14884
Keywords: Classical moment problem, Hamburger moment sequence, Stieltjes moment sequence, Hausdorff moment sequence, binomial transform, continued fraction
Received by editor(s): March 29, 2019
Received by editor(s) in revised form: September 24, 2019
Published electronically: January 29, 2020
Additional Notes: This research was supported in part by Engineering and Physical Sciences Research Council grant EP/N025636/1.
Communicated by: Stephan Ramon Garcia
Article copyright: © Copyright 2020 American Mathematical Society