Formal and numerical processes of summation of series solutions of differential equations (Q1898390)

The theories of \(k\)-summability (see [\textit{J. P. Ramis}, Lecture Notes in Physics 126, Springer (1980)]) and multisummability (see [\textit{J. Thomann}, Journées de printemps de la PRC Math-Info (1990)]) of formal power series solutions of differential equations lead to efficient computation methods. The author considers some aspects of the computation of the coefficients and of the sums of these series. He makes an essential use of computer algebra tools in order to control numerical processes.