Abstract
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.
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 163, No. 2, pp. 299–313, May, 2010.
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Candelpergher, B., Grandou, T. The renormalizing series of some integral equations. Theor Math Phys 163, 653–665 (2010). https://doi.org/10.1007/s11232-010-0048-9
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DOI: https://doi.org/10.1007/s11232-010-0048-9