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Search: MSC category 40B05 ( Multiple sequences and series (should also be assigned at least one other classification number in this section) )

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1. CJM 2010 (vol 63 pp. 241)

Essouabri, Driss; Matsumoto, Kohji; Tsumura, Hirofumi
Multiple Zeta-Functions Associated with Linear Recurrence Sequences and the Vectorial Sum Formula
We prove the holomorphic continuation of certain multi-variable multiple zeta-functions whose coefficients satisfy a suitable recurrence condition. In fact, we introduce more general vectorial zeta-functions and prove their holomorphic continuation. Moreover, we show a vectorial sum formula among those vectorial zeta-functions from which some generalizations of the classical sum formula can be deduced.

Keywords:Zeta-functions, holomorphic continuation, recurrence sequences, Fibonacci numbers, sum formulas
Categories:11M41, 40B05, 11B39

2. CJM 2005 (vol 57 pp. 941)

Berg, Christian; Durán, Antonio J.
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 $(1+1/2+\dots +1/(n+1))^{-1}$.

Categories:44A60, 40B05

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