Definition:Gelfond's Constant

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Gelfond's constant is the number obtained by raising Euler's number $e$ to the power of $\pi$ (pi):


Its decimal expansion gives its value to be approximately:

$e^\pi \approx 23 \cdotp 14069 \, 26327 \, 79269 \, 00572 \, 90863 \, 67948 \, 54738 \ldots$

This sequence is A039661 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Also see

  • Results about Gelfond's constant can be found here.

Source of Name

This entry was named for Alexander Osipovich Gelfond.

Historical Note

The Gelfond's constant arises in the context of the $7$th problem of the Hilbert $23$.

It was proved to be transcendental in $1929$ by Alexander Osipovich Gelfond.

It was since determined to be a special case of the Gelfond-Schneider Theorem, established $\text {1934}$ – $\text {1935}$.