Geodesic
Generating Asymptotics for Factorially Divergent Sequences
Séminaire lotharingien de combinatoire, 78B (2017)

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The algebraic properties of formal power series with factorial growth which admit a certain well-behaved asymptotic expansion are discussed. These series form a subring of R[[x]] which is closed under composition. An "asymptotic derivation" is defined which maps a power series to its asymptotic expansion. Leibniz and chain rules for this derivation are deduced. With these rules asymptotic expansions of implicitly defined power series can be obtained. The full asymptotic expansions of the number of connected chord diagrams and the number of simple permutations are given as examples. 

@article{SLC_2017_78B_a27,
     author = {Michael Borinsky},
     title = {Generating {Asymptotics} for {Factorially} {Divergent} {Sequences}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a27/}
}
TY  - JOUR
AU  - Michael Borinsky
TI  - Generating Asymptotics for Factorially Divergent Sequences
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a27/
ID  - SLC_2017_78B_a27
ER  - 
%0 Journal Article
%A Michael Borinsky
%T Generating Asymptotics for Factorially Divergent Sequences
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a27/
%F SLC_2017_78B_a27
Michael Borinsky. Generating Asymptotics for Factorially Divergent Sequences. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a27/