Open Problems
- Among the numbers whose geometric mean of the coefficients ai in the continued fraction expansion apparently (based on numerical evidence) tends to Khinchin's constant are π, the Euler–Mascheroni constant γ, and Khinchin's constant itself. However, none of these limits has been rigorously established, even though it is known that almost all real numbers have this property.
- It is not known if Khinchin's constant is a rational, algebraic irrational or transcendental number.
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