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Shift Transformation


The transformation

T(x)=frac(1/x)
(1)
=1/x-|_1/x_|,
(2)

where frac(x) is the fractional part of x and |_x_| is the floor function, that takes a continued fraction [a_1,a_2,...] to [a_2,a_3,...].


See also

Gauss-Kuzmin-Wirsing Constant

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References

Viader, P.; Paradis, J.; and Bibiloni, L. "A New Light on Minkowski's ?(x) Function." J. Number Th. 73, 212-227, 1998.

Referenced on Wolfram|Alpha

Shift Transformation

Cite this as:

Weisstein, Eric W. "Shift Transformation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ShiftTransformation.html

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