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Gelfond-Schneider Constant


The Gelfond-Schneider constant is the number 2^(sqrt(2))=2.66514414... (OEIS A007507) that is known to be transcendental by Gelfond's theorem. Both the Gelfand-Schneider constant 2^(sqrt(2)) and Gelfond's constant e^pi were singled out in the 7th of Hilbert's problems as examples of numbers whose transcendence was an open problem (Wells 1986, p. 45).


See also

Gelfond's Constant, Gelfond's Theorem, Pythagoras's Constant

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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.

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Gelfond-Schneider Constant

Cite this as:

Weisstein, Eric W. "Gelfond-Schneider Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Gelfond-SchneiderConstant.html

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