Non-Holonomicity of Sequences Defined via Elementary Functions
组合数学
2007-05-23 v1
摘要
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 . Moreover, we show that the sequence that arises from evaluating the Riemann zeta function at odd integers is not holonomic.
引用
@article{arxiv.math/0605142,
title = {Non-Holonomicity of Sequences Defined via Elementary Functions},
author = {Jason P. Bell and Stefan Gerhold and Martin Klazar and Florian Luca},
journal= {arXiv preprint arXiv:math/0605142},
year = {2007}
}