Geodesic
On the non-holonomic character of logarithms, powers, and the \(n\)th prime function
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2

Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website

Zbl arXiv EuDML
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 [El. J. Comb. 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.
DOI : 10.37236/1894
Classification : 05A15, 11B83, 33E30
Mots-clés : holonomic sequence, \(P\)-recursive sequence, generating function, singularities 
Philippe Flajolet; Stefan Gerhold; Bruno Salvy. On the non-holonomic character of logarithms, powers, and the \(n\)th prime function. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1894
@article{10_37236_1894,
     author = {Philippe Flajolet and Stefan Gerhold and Bruno Salvy},
     title = {On the non-holonomic character of logarithms, powers, and the \(n\)th prime function},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {2},
     doi = {10.37236/1894},
     zbl = {1076.05004},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1894/}
}
TY  - JOUR
AU  - Philippe Flajolet
AU  - Stefan Gerhold
AU  - Bruno Salvy
TI  - On the non-holonomic character of logarithms, powers, and the \(n\)th prime function
JO  - The electronic journal of combinatorics
PY  - 2004
VL  - 11
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.37236/1894/
DO  - 10.37236/1894
ID  - 10_37236_1894
ER  - 
%0 Journal Article
%A Philippe Flajolet
%A Stefan Gerhold
%A Bruno Salvy
%T On the non-holonomic character of logarithms, powers, and the \(n\)th prime function
%J The electronic journal of combinatorics
%D 2004
%V 11
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/1894/
%R 10.37236/1894
%F 10_37236_1894

Cité par Sources :