Jason P. Bell, Stefan Gerhold, Martin Klazar, Florian Luca
Published 2006-05-05Version 1
We present a new method for proving non-holonomicity of sequences, which is based on results about the number of zeros of elementary and of analytic functions. Our approach is applicable to sequences that are defined as the values of an elementary function at positive integral arguments. We generalize several recent results; e.g., non-holonomicity of the logarithmic sequence is extended to rational functions involving $\log n$. Moreover, we show that the sequence that arises from evaluating the Riemann zeta function at odd integers is not holonomic.
Summation of Hyperharmonic Series
Non-holonomicity of the sequence $\log 1, \log 2, \log 3, ...$
An Asymptotic Form of the Generating Function $\prod_{k=1}^\infty (1+x^k/k)$
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