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# Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers

Published:2005-10-01
Printed: Oct 2005
• Christian Berg
• Antonio J. Durán
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## Abstract

We introduce some non-linear transformations from the set of Hausdorff moment sequences into itself; among them is the one defined by the formula: $T((a_n)_n)=1/(a_0+\dots +a_n)$. 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 $(1+1/2+\dots +1/(n+1))^{-1}$.
 MSC Classifications: 44A60 - Moment problems 40B05 - Multiple sequences and series (should also be assigned at least one other classification number in this section)