Some Tauberian theory for the q-Lagrange inversion
Combinatorics
2013-12-30 v1 Classical Analysis and ODEs
Abstract
We consider formal power series defined through the functional q-equation of the q-Lagrange inversion. Under some assumptions, we obtain the asymptotic behavior of the coefficients of these power series. As a by-product, we show that, via the 1/q-Borel transform, the q-Lagrange inversion formula provides an interpolation between the usual Lagrange inversion (q=1) and the probabilistic theory of renewal sequences (q tends to 0). We also discuss some new solutions of the q-Lagrange inversion equation which do not vanish at 0.
Keywords
Cite
@article{arxiv.1312.6899,
title = {Some Tauberian theory for the q-Lagrange inversion},
author = {Ph. Barbe and W. P. McCormick},
journal= {arXiv preprint arXiv:1312.6899},
year = {2013}
}
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46 pages