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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, 40B05 show english descriptions Moment problems
Multiple sequences and series (should also be assigned at least one other classification number in this section)
44A60 - Moment problems
40B05 - Multiple sequences and series (should also be assigned at least one other classification number in this section)
 

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