Mathematics – Combinatorics
Scientific paper
2005-01-22
The Electronic Journal of Combinatorics, vol. 11, no. 2, article A2. 2005.
Mathematics
Combinatorics
13 pages
Scientific paper
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.
Flajolet Philippe
Gerhold Stefan
Salvy Bruno
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