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Presents an introduction to the properties of analytic functions. This title provides examples of functional equations to show how analytic solutions can be found. It treats analytic functions as those generated by sequences with positive radii of convergence.
Analytic functions. --- Functional equations. --- Power series. --- Series, Power --- Equations, Functional --- Functional analysis --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Functions of complex variables --- Series, Taylor's
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Existence and nonexistence of roots of functions involving one or more parameters has been the subject of numerous investigations. For a wide class of functions called quasi-polynomials, the above problems can be transformed into the existence and nonexistence of tangents of the envelope curves associated with the functions under investigation. In this book, we present a formal theory of the Cheng-Lin envelope method, which is completely new, yet simple and precise. This method is both simple - since only basic Calculus concepts are needed for understanding - and precise, since necessary and s
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