Geodesic
The~renormalizing series of some integral equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 2, pp. 299-313

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We consider integral equations for which the perturbation expansion gives a power series in a parameter $h$ whose coefficients are divergent integrals. We eliminate the divergent integrals by introducing a renormalizing $Z(t,h)$ series in the minimal subtraction scheme. We investigate the convergence of the formal $Z$ series in relation to the kernels of the integral equations. We find a relation of the renormalizing series to the Lagrange inversion series and also some other relations.
Keywords: renormalization, divergent integral
Mots-clés : Lagrange inversion formula. 
@article{TMF_2010_163_2_a5,
     author = {B. Candelpergher and T. Grandou},
     title = {The~renormalizing series of some integral equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {299--313},
     publisher = {mathdoc},
     volume = {163},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a5/}
}
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B. Candelpergher; T. Grandou. The~renormalizing series of some integral equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 2, pp. 299-313. http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a5/