Gelfond-Schneider Constant

The Gelfond-Schneider constant is the number  (OEIS A007507) that is known to be transcendental by Gelfond's theorem. Both the Gelfand-Schneider constant  and Gelfond's constant  were singled out in the 7th of Hilbert's problems as examples of numbers whose transcendence was an open problem (Wells 1986, p. 45).

REFERENCES:

Courant, R. and Robbins, H. What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, p. 107, 1996.

Sloane, N. J. A. Sequence A007507/M1560 in "The On-Line Encyclopedia of Integer Sequences."

Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 45, 1986.