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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 complex values. A generalized continued fraction is an expression of the form where 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: with initial values

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  • كسر مستمر معمم
  • Generalized continued fraction
  • Fracción continua generalizada
  • Fraction continue généralisée
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  • في التحليل العقدي، فرعا من الرياضيات, كسر مستمر معمم هو تعميم للكسور المستمرة الاعتيادية حيث تأخذ مقاماته وبسوطه قيما حقيقية أو عقدية ما. يأخذ الكسر المستمر المعمم الشكل التالي: حيث تسمى الأعداد an بسوطا جزئية وتسمى الأعداد bn مقامات جزئية. بالنسبة للكسور المستمرة الاعتيادية، تكون البسوط الجزئية كلها مساوية ل 1.
  • En mathématiques, une fraction continue généralisée est une expression de la forme : comportant un nombre fini ou infini d'étages. C'est donc une généralisation des fractions continues simples puisque dans ces dernières, tous les ai sont égaux à 1.
  • 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 complex values. A generalized continued fraction is an expression of the form where 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: with initial values
  • En análisis complejo, una rama de las matemáticas, una fracción continua generalizada o fracción fractal es una generalización de una fracción continua en la cual los numeradores parciales y los denominadores parciales pueden tomar cualesquiera valores reales o complejos.​ Una fracción continua generalizada es una expresión de la forma: donde los an (n > 0) son los numeradores parciales, los bn son los denominadores parciales y el término principal b0 es el llamado parte entera de la fracción continua. Las convergentes sucesivas de la fracción continua se forma aplicando las :
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  • "Exact" continued fraction for Pi
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