Engel Expansion

(Mathematical Analysis)


Mathematical Analysis
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What is Engel expansion?

The Engel expansion of a positive real number x is the unique non-decreasing sequence of positive integers such that For instance, Euler's constant e has the Engel expansion 1, 1, 2, 3, 4, 5, 6, 7, 8, ... corresponding to the infinite series Rational numbers have a finite Engel expansion, while irrational numbers have an infinite Engel expansion. If x is rational, its Engel expansion provides a representation of x as an Egyptian fraction. Engel expansions are named after Friedrich Engel, who studied them in 1913. An expansion analogous to an Engel expansion, in which alternating terms are negative, is called a .

Technology Types

chemicalcomplex numbercontinued fractiondefinite quantityegyptian fractionfractionmaterialmathematical analysisrational numberreal numbersubstance


Engel series


Développement en série de Engel (fr)Engel-Entwicklung (de)Engel-expansie (nl)Espansione di Engel (it)Expansión de Engel (es)Разложение Энгеля (ru)恩格尔展开式 (zh)

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