Gelfond-Schneider constant

The Gelfond-Schneider constant $2^{\sqrt{2}}$ was one of the first numbers to be proven to be transcendental by appying Gelfond’s theorem. However, naming the constant after Gelfond and Schneider comes from Eric Weisstein, with many people preferring to refer to it simply as 2 to the power of square root of 2.

Its value in base 10 is approximately 2.66514414269022518865029724987313984827421131371. Its continued fraction representation is neither terminating nor periodic, and begins

$$2+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{72+\mathrm{\cdots }}}}}$$

Title	Gelfond-Schneider constant
Canonical name	GelfondSchneiderConstant
Date of creation	2013-03-22 18:54:36
Last modified on	2013-03-22 18:54:36
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	4
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 11J81