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Catalan's Constant Approximations


Approximations to Catalan's constant include

K approx (9/(10))^(5/6)
(1)
 approx ln(ln892)-1
(2)
 approx (1/(96))^(1/52)
(3)
 approx (4/(51))^(1/29)
(4)
 approx ln((53)/(21))-1/(102)
(5)
 approx ((5353)/(177))^(3/11)-phi
(6)

(M. Hudson, pers. comm., Nov. 19, 2004), where phi is the golden ratio, which are good to 4, 5, 6, 6, 7, 7, and 9 digits, respectively.

Other approximations include

K approx 7/9pi^(1/7)
(7)
 approx (693)/(496)-lnphi
(8)

(K. Hammond, pers. comm., Dec. 31, 2005), where phi is the golden ratio, which are good to 5 and 9 digits, respectively.


See also

Almost Integer, Catalan's Constant

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Cite this as:

Weisstein, Eric W. "Catalan's Constant Approximations." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CatalansConstantApproximations.html

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