Suppose one has a proof of the Lagrange Inversion formula in the case for power series with some nonzero radius of convergence (that is, power series which actually describe analytic functions in some neighborhood).

Is there some argument that can show, without too much extra work, that the Lagrange Inversion formula also holds for arbitrary formal power series (that is, even when the radius of convergence for the power series is zero)?

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    $\begingroup$ I don't know about direct conversion but Roman in "Umbral Calculus" mentions Henrici, P. "An algebraic proof of the Lagrange-Burmann Formula" in Journal of Mathematical Analysis. sciencedirect.com/science/article/pii/0022247X64900630 Which I have apparently overlooked. I have been working on planting Lagrange inversion in Isabelle (a formal proof system) in what I consider a intelligibly/useful form. Thanks. $\endgroup$ – rrogers Mar 13 '17 at 3:10

Wilf's "generatingfunctionology" (Academic Press, 1994) states (and proves) the formula as valid for formal power series (theorem 5.1.1, page 172).


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