Geodesic
A Ridiculously Simple and Explicit Implicit Function Theorem
Séminaire lotharingien de combinatoire, 61A (2009-2011)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

I show that the general implicit-function problem (or parametrized fixed-point problem) in one complex variable has an explicit series solution given by a trivial generalization of the Lagrange inversion formula. I give versions of this formula for both analytic functions and formal power series. 

@article{SLC_2009-2011_61A_a3,
     author = {Alan D. Sokal},
     title = {A {Ridiculously} {Simple} and {Explicit} {Implicit} {Function} {Theorem}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {61A},
     year = {2009-2011},
     url = {http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a3/}
}
TY  - JOUR
AU  - Alan D. Sokal
TI  - A Ridiculously Simple and Explicit Implicit Function Theorem
JO  - Séminaire lotharingien de combinatoire
PY  - 2009-2011
VL  - 61A
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a3/
ID  - SLC_2009-2011_61A_a3
ER  - 
%0 Journal Article
%A Alan D. Sokal
%T A Ridiculously Simple and Explicit Implicit Function Theorem
%J Séminaire lotharingien de combinatoire
%D 2009-2011
%V 61A
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a3/
%F SLC_2009-2011_61A_a3
Alan D. Sokal. A Ridiculously Simple and Explicit Implicit Function Theorem. Séminaire lotharingien de combinatoire, 61A (2009-2011). http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a3/