Addressing the question how to "sum" a power series in one variable when it diverges that is how to attach to it analytic functions the volume gives answers by presenting & comparing the various theories of k-summability & multisummability These theories apply in particular to all solutions of ordinary differential equations The volume
Includes:: applications examples & revisits from a cohomological point of view the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1 With a view to applying the theories to solutions of differential equations a detailed survey of linear ordinary differential equations is provided which
Includes:: Gevrey asymptotic expansions Newton polygons index theorems & Sibuya's proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations This volume is the second in a series of three entitled Divergent Series Summability & Resurgence It is aimed at graduate students & researchers in mathematics & theoretical physics who are interested in divergent series Although closely related to the other two volumes it can be read independently