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Numerical Continued Fractions

  • Reza N. Jazar
Chapter
  • 26 Downloads

Abstract

In this chapter we review the method of continued fractions to show its advantage and application. Convergence and its usefulness in working with irrational numbers, as well as converting a numerical series to continued fraction back and forth are the topics of this chapter. This review makes the reader ready to derive and work with solution of differential equations in continued fractions.

We will show that all real numbers may be divided into rational and irrational. They also may be divided into algebraic and transcendental. A rational number can be expressed by a fraction of the form p/q where p and q are integers. Numbers are also either algebraic or transcendental. The method expressing rational and irrational numbers by continued fractions will be covered in this chapter to make the reader ready to solve differential equations in continued fractions.

Keywords

Continued fractions Conversion of series to continued fractions Convergents Rational numbers Irrational numbers Transcendental numbers 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  • Reza N. Jazar
    • 1
  1. 1.School of EngineeringRMIT UniversityMelbourneAustralia

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