Meanings
- mathematicsThe value e^π (approximately 23.140692632779), known to be transcendental.
and we have the promised appearance of Gelfond's constant.
2007, Julian Havil, Nonplussed!: Mathematical Proof of Implausible Ideas, Princeton University Press, page 143, This means that ∑ₙₑᵥₑₙV_n(1)=∑ₘ₌₁ ᪲V_2m(1)=∑ₘ₌₁ ᪲(πᵐ)/(m!)=e^π-12 more examples
2009, Samuel W. Gilbert, The Riemann Hypothesis and the Roots of the Riemann Zeta Function, BookSurge Publishing, page 93, Gelfond's constant satisfies the identity e^π=(-1)⁻ⁱ Therefore, the roots of the Riemann zeta function are defined by geometrical constraints of the discrete partial sums of the Dirichlet series terms by continuous and geometrically equivalent envelopes defined by powers of Gelfond's constant.
2016, Ravi P. Agarwal, Hans Agarwal, Syamal K. Sen, Birth, growth and computation of pi to ten trillion digits, David H. Bailey, Jonathan M. Borwein (editors, Pi: The Next Generation, Springer, page 403, Alexander Osipovich Gelfond (1906-1968) was a Soviet mathematician. He proved that e^π (Gelfond's constant) is transcendental, but nothing yet is known about the nature of the numbers π + e, πe, or πᵉ.
Origin
After Soviet mathematician Алекса́ндр О́сипович Ге́льфонд (Alexander Osipovich Gelfond).
Full word history & related roots →Cite this entry
Gelfond's constant. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Gelfond's%20constant
“Gelfond's constant.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Gelfond's%20constant. Accessed November 4, 2026.
WatkinsX Dictionary, s.v. “Gelfond's constant,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Gelfond's%20constant.
Source: Gelfond's constant on Wiktionary, CC BY-SA 4.0.