Continued fraction

<p>A continued fraction is a <a href="/facts/Expression_(mathematics)/MPrMlYbE">mathematical expression</a> that can be written as a <a href="/facts/Fraction/ghnQE9B3">fraction</a> with a <a href="/facts/Denominator/ghnQE9B3">denominator</a> that is a sum that contains another simple or continued fraction. Depending on whether this <a href="/facts/Iteration/AMc1p7BL">iteration</a> terminates with a simple fraction or not, the continued fraction is finite or infinite.
</p><p>Different fields of <a href="/facts/Mathematics/pxTouaz4">mathematics</a> have different terminology and notation for continued fraction.  In <a href="/facts/Number_theory/zhoa7zrc">number theory</a> the standard unqualified use of the term continued fraction  refers to the special case where all numerators are 1, and is treated in the article <a href="/facts/Simple_continued_fraction/Wg1cMPxN">simple continued fraction</a>. The present article treats the case where <a href="/facts/Numerator/ghnQE9B3">numerators</a> and <a href="/facts/Denominator/ghnQE9B3">denominators</a> are sequences 
  
    
      
        {
        
          a
          
            i
          
        
        }
        ,
        {
        
          b
          
            i
          
        
        }
      
    
    {\displaystyle \{a_{i}\},\{b_{i}\}}
  
 of constants or functions. 
From the perspective of number theory, these are called generalized continued fraction. From the perspective of <a href="/facts/Complex_analysis/hgCoQlH0">complex analysis</a> or <a href="/facts/Numerical_analysis/QT9cYa9z">numerical analysis</a>, however, they are just standard, and in the present article they will simply be called "continued fraction".
</p>

Continued fraction open-in-new

Continued fraction