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A different characterization of multi-summable power series. (English) Zbl 0759.40005
Author’s abstract: “Given \(k_ 1>k_ 2>k_ 3>\dots>k_ p>0\) and a real number \(d\), it is shown that a formal power series \(\hat f\) is \((k_ 1,\dots,k_ p)\)-summable in direction \(d\) if and only if \(\hat f\) can be decomposed into a sum of formal series \(\hat f_ j\) (which may be series in a root of \(z\), unless we restrict to \(k_ p\geq{1\over 2}\)), so that each \(\hat f_ j\) is \(k_ j\)-summable in direction \(d\), for \(j=1,\dots,p\)”.

40C15 Function-theoretic methods (including power series methods and semicontinuous methods) for summability
34E05 Asymptotic expansions of solutions to ordinary differential equations
30E15 Asymptotic representations in the complex plane