Continued Fractions

  • Calvin D. Ahlbrandt
  • Allan C. Peterson
Part of the Kluwer Texts in the Mathematical Sciences book series (TMS, volume 16)


Riccati equations of the form developed in the previous chapter are closely related to continued fractions. With the connections between these subjects as our goal, we make a fresh start in neutral notation. Recall some basic facts about linear fractional (Möbius) transformations. Suppose that A is a nonsingular 2 × 2 matrix
$$A = \left[ {\begin{array}{*{20}{c}} a & b \\ c & d \\ \end{array} } \right]$$
with real or complex entries. The associated linear fractional transformation is formally defined by
$${T_A}(z) = \frac{{az + b}}{{cz + d}}$$


Riccati Equation Continue Fraction Companion Matrix Formal Composite Normed Ring 
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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Calvin D. Ahlbrandt
    • 1
  • Allan C. Peterson
    • 2
  1. 1.University of MissouriUSA
  2. 2.University of NebraskaUSA

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