On the non-holonomic character of logarithms, powers, and the n-th prime function
Combinatorics
2008-02-28 v1
Abstract
We establish that the sequences formed by logarithms and by "fractional" powers of integers, as well as the sequence of prime numbers, are non-holonomic, thereby answering three open problems of Gerhold [Electronic Journal of Combinatorics 11 (2004), R87]. Our proofs depend on basic complex analysis, namely a conjunction of the Structure Theorem for singularities of solutions to linear differential equations and of an Abelian theorem. A brief discussion is offered regarding the scope of singularity-based methods and several naturally occurring sequences are proved to be non-holonomic.
Keywords
Cite
@article{arxiv.math/0501379,
title = {On the non-holonomic character of logarithms, powers, and the n-th prime function},
author = {Philippe Flajolet and Stefan Gerhold and Bruno Salvy},
journal= {arXiv preprint arXiv:math/0501379},
year = {2008}
}
Comments
13 pages