Non-Holonomicity of Sequences Defined via Elementary Functions

Details Non-Holonomicity of Sequences Defined via Elementary Functions Non-Holonomicity of Sequences Defined via Elementary Functions

2006-05-05

arxiv.org/abs/math/0605142v1

Mathematics

Combinatorics

Scientific paper

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.

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