Geodesic
Lindelöf representations and (non-)holonomic sequences
The electronic journal of combinatorics, Tome 17 (2010)
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Various sequences that possess explicit analytic expressions can be analysed asymptotically through integral representations due to Lindelöf, which belong to an attractive but somewhat neglected chapter of complex analysis. One of the outcomes of such analyses concerns the non-existence of linear recurrences with polynomial coefficients annihilating these sequences, and, accordingly, the non-existence of linear differential equations with polynomial coefficients annihilating their generating functions. In particular, the corresponding generating functions are transcendental. Asymptotic estimates of certain finite difference sequences come out as a byproduct of the Lindelöf approach.
DOI : 10.37236/275
Classification : 05A15, 05A19
Mots-clés : holonomic sequence, P-recursive, analytic combinatorics 
@article{10_37236_275,
     author = {Philippe Flajolet and Stefan Gerhold and Bruno Salvy},
     title = {Lindel\"of representations and (non-)holonomic sequences},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/275},
     zbl = {1222.05005},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/275/}
}
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Philippe Flajolet; Stefan Gerhold; Bruno Salvy. Lindelöf representations and (non-)holonomic sequences. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/275

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