# Iversen theorem

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If is an isolated essential singularity of an analytic function of a complex variable , then every exceptional value in the sense of E. Picard is an asymptotic value of at . For example, the values and are exceptional and asymptotic values of at the essential singularity . This result of F. Iversen [1] supplements the big Picard theorem on the behaviour of an analytic function in a neighbourhood of an essential singularity.

#### References

 [1] F. Iversen, "Récherches sur les fonctions inverses des fonctions méromorphes" , Helsinki (1914) [2] E.F. Collingwood, A.J. Lohwater, "The theory of cluster sets" , Cambridge Univ. Press (1966) pp. Chapt. 1;6