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mass
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(none)
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<math>k \in \{1,2,\ldots\}</math>
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<math>-\log_2\left 1- rac{1}{(k+1)^2}
ight </math>
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<math>1 - \log_2 + 2\,\log_2[(k+1)! - \log_2[(k+2)!]</math>
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(not defined)
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<math>2\,</math>
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<math>1\,</math>
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(not defined)
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(not defined)
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(not defined)
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<math>343\,</math>{{cite journal
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In
Mathematics , the gives the
Probability Distribution of the occurrence of a given
Integer in the
Continued Fraction expansion of an arbitrary
Real Number . The distribution is named after
Carl Friedrich Gauss , who first conjectured and studied the distribution around
1800 , and
R. O. Kuz'min , who, in
1928 , along with
Paul Lévy , in
1929 , was able to prove Gauss's conjecture. Later,
K. Ivan Babenko and
Eduard Wirsing completely solved the problem, and were able to show that the speed of convergence of the continued fraction digits to the limiting distribution was exponential.
The
Probability that any term
in a continued fraction expansion is equal to ''k'' is given by
:
