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The concept of moment differentiation is extended to the class of momentsummable functions, giving rise to moment differential properties. The mainresult leans on accurate upper estimates for the integral representation of themoment derivatives of functions under exponential-like growth at infinity, andappropriate deformation of the integration paths. The theory is applied toobtain summability results of certain family of generalized linear momentpartial differential equations with variable coefficients.

Summability of formal solutions for some generalized moment partial differential equations