A curious approximation to theFeigenbaum constant is given by

(1)

where isGelfond's constant, which is good to 6 digits to the right of thedecimal point.

M. Trott (pers. comm., May 6, 2008) noted

(2)

where isGauss's constant, which is good to 4 decimal digits, and

(3)

where is thetetranacci constant, which is good to 3 decimal digits.

A strange approximation good to five digits is given by the solution to

(4)

which is

(5)

where is theLambert W-function (G. Deppe, pers. comm., Feb. 27, 2003).

(6)

gives to 3 digits (S. Plouffe, pers. comm., Apr. 10, 2006).

M. Hudson (pers. comm., Nov. 20, 2004) gave

			(7)
			(8)
			(9)

which are good to 17, 13, and 9 digits respectively.

Stoschek gave the strange approximation

(10)

which is good to 9 digits.

R. Phillips (pers. comm., Sept. 14, 2004-Jan. 25, 2005) gave the approximations

			(11)
			(12)
			(13)
			(14)
			(15)
			(16)

wheree is the base of thenatural logarithm and isGelfond's constant, which are good to 3, 3, 5, 7, 9, and 10 decimal digits, respectively, and

			(17)
			(18)
			(19)
			(20)
			(21)
			(22)
			(23)

which are good to 3, 3, 3, 4, 6, 8, and 8 decimal digits, respectively.

An approximation to due to R. Phillips (pers. comm., Jan. 27, 2005) is obtained by numerically solving

(24)

for, where is thegolden ratio, which is good to 4 digits.

See also

Explore with Wolfram|Alpha

More things to try:

• feigenbaum constant approximations
• {1/4, -1/2, 1} cross {1/3, 1, -2/3}
• ellipse with semiaxes 2,5 centered at (3,0)

References

Referenced on Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Feigenbaum Constant Approximations."FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/FeigenbaumConstantApproximations.html

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