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1: 1.10 Functions of a Complex Variable
Then z = z 0 is an isolated singularity of f ( z ) . …Lastly, if a n 0 for infinitely many negative n , then z 0 is an isolated essential singularity. … In any neighborhood of an isolated essential singularity, however small, an analytic function assumes every value in with at most one exception. …
2: 32.2 Differential Equations
be a nonlinear second-order differential equation in which F is a rational function of w and d w / d z , and is locally analytic in z , that is, analytic except for isolated singularities in . …An equation is said to have the Painlevé property if all its solutions are free from movable branch points; the solutions may have movable poles or movable isolated essential singularities (§1.10(iii)), however. …