Applications of Gelfond's constant

Asked Aug 27 '17 at 08:10

Active Aug 27 '17 at 08:20

Viewed 309 times

Gelfond's constant is the transcendental number $e^\pi$ which is approximately equal to:

$$ 23.140692632... $$

Are there any useful (real-world) applications of this constant besides its appearance in the Gelfond-Schneider Theorem? Is is "used" in some field of mathematics in a productive manner?

edited Aug 27 '17 at 08:20

Jyrki Lahtonen

133,153

asked Aug 27 '17 at 08:10

Klangen

5,075

3

Nope, there is no use. – MCCCS Aug 27 '17 at 08:17
3

You can use it to calculate the volume of the n-dimensional ball. – Mr. Xcoder Aug 27 '17 at 08:29
1

@Mr.Xcoder: Not really. It is (somewhat trivially) the sum of the volumes of the $2n$-dimensional unit ball balls over all $n\ge 1$, but (a) that is not particularly useful for calculating any of the individual volumes, and (b) adding volumes of different dimensions is of questionable meaningfulness anyway. – hmakholm left over Monica Aug 27 '17 at 08:37
(correction: you need the $(2\cdot 0)$-dimensional unit ball, whose $0$-volume is $1$, too, or you get $e^\pi-1$). – hmakholm left over Monica Aug 27 '17 at 08:49
1

This value can lead $(-1)^i=0.0432139182・・・$. – Takahiro Waki Aug 27 '17 at 09:28

Applications of Gelfond's constant

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