Last Updated
：2025/12/04
Euler's continued fraction formula
Proper noun
Japanese Meaning
数学において、有限個の積の総和と有限連分数との関係を示す公式。すなわち、a₀＋a₀a₁＋a₀a₁a₂＋⋯＋a₀a₁a₂⋯aₙと、a₀の数値から始まる連分数表現の間に成り立つ関係を表す。
Quizzes for review
(mathematics) A formula connecting a finite sum of products to a finite continued fraction: a_0+a_0a_1+a_0a_1a_2+⋯+a_0a_1a_2⋯a_n= cfrac a_0 1- cfrac a_1 1+a_1- cfrac a_2 1+a_2- cfrac ddotsddots cfrac a_n-1 1+a_n-1- cfrac a_n 1+a_n,.
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Euler's continued fraction formula
When teaching advanced undergraduates, I often illustrate Euler's continued fraction formula with a simple example to show how a finite sum of products can be written as a continued fraction.
See correct answer
When teaching advanced undergraduates, I often illustrate Euler's continued fraction formula with a simple example to show how a finite sum of products can be written as a continued fraction.
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