Gelfond's constant
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In mathematics, Gelfond's constant, named after Aleksandr Gelfond, is
that is, e to the power of π. Like both e and π, this constant is a transcendental number. This can be proven by Gelfond's theorem and noting the fact that
where i is the imaginary unit. Since −i is algebraic, but certainly not rational, eπ is transcendental. The constant was mentioned in Hilbert's seventh problem. A related constant is 
, known as the Gelfond–Schneider constant. The related value 
is also irrational[1].
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[edit] Numerical value
In decimal form, the constant evaluates as
Its numerical value can be found with the iteration
where 
After N iterations, the approximation is given by
[edit] Numerical coincidences
The number
[edit] See also
[edit] External links
[edit] References
- ^ Nesterenko, Yu. "Modular Functions and Transcendence Problems." C. R. Acad. Sci. Paris Sér. I Math. 322, 909-914, 1996.
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