# Asymptotic stability for sets of polynomials

Thomas W. Müller; Jan-Christoph Schlage-Puchta

Archivum Mathematicum (2005)

- Volume: 041, Issue: 2, page 151-155
- ISSN: 0044-8753

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topMüller, Thomas W., and Schlage-Puchta, Jan-Christoph. "Asymptotic stability for sets of polynomials." Archivum Mathematicum 041.2 (2005): 151-155. <http://eudml.org/doc/249491>.

@article{Müller2005,

abstract = {We introduce the concept of asymptotic stability for a set of complex functions analytic around the origin, implicitly contained in an earlier paper of the first mentioned author (“Finite group actions and asymptotic expansion of $e^\{P(z)\}$", Combinatorica 17 (1997), 523 – 554). As a consequence of our main result we find that the collection of entire functions $\exp (\mathfrak \{P\})$ with $\mathfrak \{P\}$ the set of all real polynomials $P(z)$ satisfying Hayman’s condition $[z^n]\exp (P(z))>0\,(n\ge n_0)$ is asymptotically stable. This answers a question raised in loc. cit.},

author = {Müller, Thomas W., Schlage-Puchta, Jan-Christoph},

journal = {Archivum Mathematicum},

keywords = {power series; coefficients; asymptotic expansion; power series; coefficients; asymptotic expansion},

language = {eng},

number = {2},

pages = {151-155},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Asymptotic stability for sets of polynomials},

url = {http://eudml.org/doc/249491},

volume = {041},

year = {2005},

}

TY - JOUR

AU - Müller, Thomas W.

AU - Schlage-Puchta, Jan-Christoph

TI - Asymptotic stability for sets of polynomials

JO - Archivum Mathematicum

PY - 2005

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 041

IS - 2

SP - 151

EP - 155

AB - We introduce the concept of asymptotic stability for a set of complex functions analytic around the origin, implicitly contained in an earlier paper of the first mentioned author (“Finite group actions and asymptotic expansion of $e^{P(z)}$", Combinatorica 17 (1997), 523 – 554). As a consequence of our main result we find that the collection of entire functions $\exp (\mathfrak {P})$ with $\mathfrak {P}$ the set of all real polynomials $P(z)$ satisfying Hayman’s condition $[z^n]\exp (P(z))>0\,(n\ge n_0)$ is asymptotically stable. This answers a question raised in loc. cit.

LA - eng

KW - power series; coefficients; asymptotic expansion; power series; coefficients; asymptotic expansion

UR - http://eudml.org/doc/249491

ER -

## References

top- Dress A., Müller T., Decomposable functors and the exponential principle, Adv. in Math. 129 (1997), 188–221. (1997) Zbl0947.05002MR1462733
- Hayman W., A generalisation of Stirling’s formula, J. Reine u. Angew. Math. 196 (1956), 67–95. (196) MR0080749
- Müller T., Finite group actions and asymptotic expansion of ${e}^{P\left(z\right)}$, Combinatorica 17 (1997), 523–554. (1997) MR1645690
- Stanley R. P., Enumerative Combinatorics, vol. 2, Cambridge University Press, 1999. (1999) Zbl0945.05006MR1676282

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