Description

Book Synopsis
This book presents a self-contained and unified introduction to the properties of analytic functions. Based on recent research results, it provides many examples of functional equations to show how analytic solutions can be found.Unlike in other books, analytic functions are treated here as those generated by sequences with positive radii of convergence. By developing operational means for handling sequences, functional equations can then be transformed into recurrence relations or difference equations in a straightforward manner. Their solutions can also be found either by qualitative means or by computation. The subsequent formal power series function can then be asserted as a true solution once convergence is established by various convergence tests and majorization techniques. Functional equations in this book may also be functional differential equations or iterative equations, which are different from the differential equations studied in standard textbooks since composition of known or unknown functions are involved.

Table of Contents
Prologue; Sequences; Power Series Functions; Functional Equations without Differentiation; Functional Equations with Differentiation; Functional Equations with Iteration.

Analytic Solutions Of Functional Equations

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    A Hardback by Sui Sun Cheng, Wenrong Li

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      Book details

      Publisher World Scientific Publishing Co Pte Ltd
      Published 18 March 2008
      ISBN-13 9789812793348
      978-9812793348
      ISBN-10 9812793348

      Description

      Book Synopsis
      This book presents a self-contained and unified introduction to the properties of analytic functions. Based on recent research results, it provides many examples of functional equations to show how analytic solutions can be found.Unlike in other books, analytic functions are treated here as those generated by sequences with positive radii of convergence. By developing operational means for handling sequences, functional equations can then be transformed into recurrence relations or difference equations in a straightforward manner. Their solutions can also be found either by qualitative means or by computation. The subsequent formal power series function can then be asserted as a true solution once convergence is established by various convergence tests and majorization techniques. Functional equations in this book may also be functional differential equations or iterative equations, which are different from the differential equations studied in standard textbooks since composition of known or unknown functions are involved.

      Table of Contents
      Prologue; Sequences; Power Series Functions; Functional Equations without Differentiation; Functional Equations with Differentiation; Functional Equations with Iteration.

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