Wyler's constant is defined as
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
(Wyler 1969, 1971; OEIS A180872 and A180873), which at the time it was proposed, agreed with experiment to within 
ppm for the value of the fine structure constant 
in physics. The current best value
for 
is given by
 |
(4)
|
(Hanneke et al. 2008).
While it appears to have a connection with the invariance group of a relativistic quantum theoretical wave equation, a number of errors in Wyler's papers are cited in Robertson (1971). Robertson (1971) also notes, "It is appealing to think that it [the fine-structure constant] might be derivable theoretically. Wyler's number ... appears to have better chances to be derived from a theory than any of the other numbers that also agree with experiment. It may be that even though the expression (8) [from Wyler's paper] is not correct, the number (12) [Wyler's constant] somehow is correct." Adler (1972) terms the constant, "a number in search of a theory" and notes that "whether the agreement of Eq. (23) [Wyler's constant] with experiment has a basis in physics, or is purely fortuitous, remains at present a completely open question."
Kragh (2003) summarized the history of conjectured closed expressions for the fine structure constant, though does not mention Wyler's form.
." Phys. Rev. Lett. 28, 462-464, 1972.Hanneke,
D.; Fogwell, S.; and Gabrielse, G. "New Measurement of the Electron Magnetic
Moment and the Fine Structure Constant." Phys. Rev. Lett. 100,
120801 (4 pages), 2008.Kragh, H. "Magic Number: A Partial History
of Fine-Structure Constant." Arch. Hist. Exact Sci. 57, 395-431,
2003.Lubkin, G. B. "A Mathematician's Version of the Fine-Structure
Constant."Physics Today 24, No. 8, 17-19, 1971.Robertson,
B. "Wyler's Expression for the Fine-Structure Constant 
." Phys. Rev. Lett. 27, 1545-1547, 1971.Sloane,
N. J. A. Sequences