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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on generating functions for Hausdorff moment sequences


Authors: Oliver Roth, Stephan Ruscheweyh and Luis Salinas
Journal: Proc. Amer. Math. Soc. 136 (2008), 3171-3176
MSC (2000): Primary 30E05, 26A48
Published electronically: April 30, 2008
MathSciNet review: 2407081
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Abstract: For functions $ f$ whose Taylor coefficients at the origin form a Hausdorff moment sequence we study the behaviour of $ w(y):=\vert f(\gamma+iy)\vert$ for $ y>0$ ( $ \gamma\leq1$ fixed).


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Additional Information

Oliver Roth
Affiliation: Mathematisches Institut, Universität Würzburg, D-97074 Würzburg, Germany
Email: roth@mathematik.uni-wuerzburg.de

Stephan Ruscheweyh
Affiliation: Mathematisches Institut, Universität Würzburg, D-97074 Würzburg, Germany
Email: ruscheweyh@mathematik.uni-wuerzburg.de

Luis Salinas
Affiliation: Departamento de Informática, Universidad Técnica F. Santa María, Valparaíso, Chile
Email: lsalinas@inf.utfsm.cl

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09460-4
PII: S 0002-9939(08)09460-4
Keywords: Hausdorff moment sequences, completely monotone sequences, Pick functions, convolution, polylogarithms
Received by editor(s): July 5, 2007
Published electronically: April 30, 2008
Additional Notes: The first and second authors acknowledge partial support from the German-Israeli Foundation (grant G-809-234.6/2003). The second and third authors received partial support from FONDECYT (grants 1070269 and 7070131) and DGIP-UTFSM (grant 240721).
Communicated by: Andreas Seeger
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.