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Abstract view

# Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers

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 $(1+1/2+\dots +1/(n+1))^{-1}$.