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Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers |
Canad. J. Math. 57(2005), 941-960
Published:2005-10-01
Printed: Oct 2005
Printed: Oct 2005
- Christian Berg
- Antonio J. Durán
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) |