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Zalcman's Lemma


Let f be a family of meromorphic functions on the unit disk D which are not normal at 0. Then there exist sequences f_n in F, z_n, rho_n, and a nonconstant function f meromorphic in the plane such that

 f_n(z_n+rho_nz)->f(z),

locally and uniformly (in the spherical sense) in the complex plane C (Schwick 2000), where z_n->0 and rho_n->0.


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References

Schwick, W. "A Note on Zalcman's Lemma." New Zealand J. Math. 29, 71-72, 2000.Zalcman, L. "A Heuristic Principle in Complex Function Theory." Amer. Math. Monthly 82, 813-817, 1975.

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Zalcman's Lemma

Cite this as:

Weisstein, Eric W. "Zalcman's Lemma." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ZalcmansLemma.html

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