Gelfond–Schneider constant
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The Gelfond–Schneider constant is
- <math>2^{\sqrt{2}}=2.6651441...</math>
which Aleksandr Gelfond proved to be a transcendental number using the Gelfond–Schneider theorem, answering one of the questions raised in Hilbert's seventh problem.
Its square root is
- <math>\sqrt{2}^{\sqrt{2}}=1.6325269...</math>
which can be used in a nonconstructive proof that an irrational number to the power of an irrational number can sometimes produce a rational number.
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