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Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers

Published online by Cambridge University Press:  20 November 2018

Christian Berg  and
Antonio J. Durán
Christian Berg
Affiliation:
Institut for Matematiske Fag., Københavns Universitet, Universitetsparken 5, DK-2100 København ø, Denmark, e-mail: berg@math.ku.dk
Antonio J. Durán
Affiliation:
Departamento de Análisis Matemático, Universidad de Sevilla, Apdo (P. O. BOX) 1160, 41080 Sevilla, Spain, e-mail: duran@us.es
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Abstract

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We introduce some non-linear transformations from the set of Hausdorff moment sequences into itself; among them is the one defined by the formula: $T\left( {{\left( {{a}_{n}} \right)}_{n}} \right)\,=\,1/\left( {{a}_{0}}\,+\cdots +\,{{a}_{n}} \right).$ We give some examples of Hausdorff moment sequences arising from the transformations and provide the corresponding measures: one of these sequences is the reciprocal of the harmonic numbers ${{\left( 1+1/2\,+\cdots +\,1/\left( n+1 \right) \right)}^{-1}}.$

Keywords

Primary: 44A60secondary: 40B05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 5 , 01 October 2005 , pp. 941 - 960
Copyright
Copyright © Canadian Mathematical Society 2005

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