Gelfond's Constant is Transcendental/Historical Note

Historical Note on Gelfond's Constant is Transcendental

The question of the transcendental nature of Gelfond's constant $e^\pi$ was raised in the context of the $7$th problem of the Hilbert $23$.

That Gelfond's Constant is Transcendental was initially established in $1929$ by Alexander Osipovich Gelfond.

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

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2 \cdotp 665 \, 144 \ldots$
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.29$: Liouville ($\text {1809}$ – $\text {1882}$)
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.18$: Algebraic and Transcendental Numbers. $e$ is Transcendental
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2 \cdotp 66514 \, 4 \ldots$