The Engel expansion of a positive real number x is the unique non-decreasing sequence of positive integers such that
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 Pierce expansion.
Read more about Engel Expansion: Engel Expansions, Continued Fractions, and Fibonacci, Algorithm For Computing Engel Expansions, Example, Engel Expansions of Rational Numbers, Engel Expansions For Some Well-known Constants, Growth Rate of The Expansion Terms
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