
In mathematics, Cahen's constant is defined as an infinite series of unit fractions, with alternating signs, derived from Sylvester's sequence: By considering these fractions in pairs, we can also view 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 (also known for the CahenMellin integral), who first formulated and investigated its series (Cahen 1891). Cahen's constant is known to be transcendental (Davison and Shallit 1991). 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 1, 1, 2, 3, 14, 129, 25298, 420984147, ... (sequence A006279 in OEIS) defined by the recurrence then the continued fraction expansion of Cahen's constant is [0,1,q_0^2,q_1^2,q_2^2,\ldots] References * Cahen, Eugène (1891). "Note sur un développement des quantités numériques, qui présente quelque analogie avec celui en fractions continues". Nouvelles Annales de Mathématiques 10: 508–514. * Davison, J. Les; Shallit, Jeffrey O. (1991). "Continued fractions for some alternating series". Monatshefte für Mathematik 111: 119–126. doi:10.1007/BF01332350.
* Weisstein, Eric W. "Cahen's Constant". MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/CahensConstant.html. * "The Cahen constant to 4000 digits". http://pi.lacim.uqam.ca/piDATA/cahen.txt. Retrieved from "http://en.wikipedia.org/" 
