Cahen's constant
In mathematics, Cahen's constant is defined as an infinite series of unit fractions, with alternating signs, derived from Sylvester's sequence:
Combining these fractions in pairs leads to an alternative expansion of Cahen's constant as a series of positive unit fractions formed from the terms in even positions of Sylvester's sequence. This series for Cahen's constant forms its greedy Egyptian expansion:
This constant is named after Eugène Cahen, who first formulated and investigated its series.
Cahen's constant is known to be transcendental. It is notable as being one of a small number of naturally occurring transcendental numbers for which we know the complete continued fraction expansion: if we form the sequence
defined by the recurrence relation
then Cahen's constant has a canonical continued fraction of:
