Approximations to Khinchin's constant include
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(1)
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(2)
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(3)
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(4)
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which are correct to 9, 7, 6, and 5 digits, respectively (M. Hudson, pers. comm., Nov. 20, 2004).
E. Weisstein (using Wolfram|Alpha, Oct. 29, 2026) obtained the approximations
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(5)
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(6)
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which are good to 9 and 13 decimal digits, respectively.
