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Schur-Jabotinsky Theorem

Let P=a_1x+a_2x^2+... be an almost unit in the integral domain of formal power series (with a_1!=0) and define

P^k=sum_(n=k)^inftya_n^((k))x^n
(1)

for k=+/-1, +/-2, .... If Q=P^(-1), then for all positive integers m,

Q^m=sum_(n=m)^inftyb_n^((m))x^n,
(2)

where

b_n^((m))=m/na_(-m)^((-n))
(3)

for n>=m.

See also

Lagrange Inversion Theorem

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References

Henrici, P. Applied and Computational Complex Analysis, Vol. 1: Power Series-Integration-Conformal Mapping-Location of Zeros. New York: Wiley, pp. 55-56, 1988.

Referenced on Wolfram|Alpha

Schur-Jabotinsky Theorem

Cite this as:

Weisstein, Eric W. "Schur-Jabotinsky Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Schur-JabotinskyTheorem.html

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