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- Generalized_continued_fraction abstract "In complex analysis, a branch of mathematics, a generalized continued fraction is a generalization of regular continued fractions in canonical form, in which the partial numerators and partial denominators can assume arbitrary real or complex values.A generalized continued fraction is an expression of the formwhere the an (n > 0) are the partial numerators, the bn are the partial denominators, and the leading term b0 is called the integer part of the continued fraction.The successive convergents of the continued fraction are formed by applying the fundamental recurrence formulas:and in generalwhere An is the numerator and Bn is the denominator, called continuants, of the nth convergent.If the sequence of convergents {xn} approaches a limit the continued fraction is convergent and has a definite value. If the sequence of convergents never approaches a limit the continued fraction is divergent. It may diverge by oscillation (for example, the odd and even convergents may approach two different limits), or it may produce an infinite number of zero denominators Bn.".
- Generalized_continued_fraction wikiPageExternalLink index.html?pg=206.
- Generalized_continued_fraction wikiPageExternalLink 0521818052ws.pdf.
- Generalized_continued_fraction wikiPageExternalLink General%20Method%20for%20Extracting%20Roots.pdf.
- Generalized_continued_fraction wikiPageID "739199".
- Generalized_continued_fraction wikiPageRevisionID "601160225".
- Generalized_continued_fraction hasPhotoCollection Generalized_continued_fraction.
- Generalized_continued_fraction name "Exact continued fraction for Pi".
- Generalized_continued_fraction sequencenumber "A133593".
- Generalized_continued_fraction subject Category:Continued_fractions.
- Generalized_continued_fraction type Abstraction100002137.
- Generalized_continued_fraction type ComplexNumber113729428.
- Generalized_continued_fraction type ContinuedFraction113736550.
- Generalized_continued_fraction type ContinuedFractions.
- Generalized_continued_fraction type DefiniteQuantity113576101.
- Generalized_continued_fraction type Fraction113732078.
- Generalized_continued_fraction type Measure100033615.
- Generalized_continued_fraction type Number113582013.
- Generalized_continued_fraction type RationalNumber113730469.
- Generalized_continued_fraction type RealNumber113729902.
- Generalized_continued_fraction comment "In complex analysis, a branch of mathematics, a generalized continued fraction is a generalization of regular continued fractions in canonical form, in which the partial numerators and partial denominators can assume arbitrary real or complex values.A generalized continued fraction is an expression of the formwhere the an (n > 0) are the partial numerators, the bn are the partial denominators, and the leading term b0 is called the integer part of the continued fraction.The successive convergents of the continued fraction are formed by applying the fundamental recurrence formulas:and in generalwhere An is the numerator and Bn is the denominator, called continuants, of the nth convergent.If the sequence of convergents {xn} approaches a limit the continued fraction is convergent and has a definite value. ".
- Generalized_continued_fraction label "Fracción continua generalizada".
- Generalized_continued_fraction label "Fraction continue généralisée".
- Generalized_continued_fraction label "Generalized continued fraction".
- Generalized_continued_fraction label "كسر مستمر معمم".
- Generalized_continued_fraction sameAs Fracción_continua_generalizada.
- Generalized_continued_fraction sameAs Fraction_continue_généralisée.
- Generalized_continued_fraction sameAs m.0377g7.
- Generalized_continued_fraction sameAs Q4115724.
- Generalized_continued_fraction sameAs Q4115724.
- Generalized_continued_fraction sameAs Generalized_continued_fraction.
- Generalized_continued_fraction wasDerivedFrom Generalized_continued_fraction?oldid=601160225.
- Generalized_continued_fraction isPrimaryTopicOf Generalized_continued_fraction.