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We consider the valued field $\mathds{K}:=\mathbb{R}((\Gamma))$ ofgeneralized series (with real coefficients and monomials in a totally orderedmultiplicative group $\Gamma$). We investigate how to endow $\mathds{K}$ with aseries derivation, that is a derivation that satisfies some natural propertiessuch as commuting with infinite sums (strong linearity) and (an infiniteversion of) Leibniz rule. We characterize when such a derivation is of Hardytype, that is, when it behaves like differentiation of germs of real valuedfunctions in a Hardy field. We provide a necessary and sufficent condition fora series derivation of Hardy type to be surjective.

Hardy type derivations on generalized series fields