analytic function
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11: 22.17 Moduli Outside the Interval [0,1]
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§22.17(ii) Complex Moduli
…12: 1.10 Functions of a Complex Variable
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►In any neighborhood of an isolated essential singularity, however small, an analytic function assumes every value in with at most one exception.
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Analytic Functions
… ►Suppose that are analytic functions in . …13: 32.2 Differential Equations
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►be a nonlinear second-order differential equation in which is a rational function of and , and is locally analytic in , that is, analytic except for isolated singularities in .
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►in which , , , , and are locally analytic functions.
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14: 1.13 Differential Equations
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►Assume that in the equation
… and belong to domains and respectively, the coefficients and are continuous functions of both variables, and for each fixed (fixed ) the two functions are analytic in (in ).
Suppose also that at (a fixed) , and are analytic functions of .
Then at each , , and are analytic functions of .
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►The inhomogeneous (or nonhomogeneous) equation
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15: 1.9 Calculus of a Complex Variable
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Analyticity
… ►A function analytic at every point of is said to be entire. … ► … ►Inside the circle the sum of the series is an analytic function . …16: 14.21 Definitions and Basic Properties
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