Komornik-Loreti Constant
المؤلف:
Allouche, J.-P. and Cosnard, M.
المصدر:
"The Komornik-Loreti Constant Is Transcendental." Amer. Math. Monthly 107
الجزء والصفحة:
...
2-3-2020
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Komornik-Loreti Constant
The Komornik-Loreti constant is the value 
such that
 |
(1)
|
where ![<span style=]()
{t_k}" src="http://mathworld.wolfram.com/images/equations/Komornik-LoretiConstant/Inline2.gif" style="height:15px; width:20px" /> is the Thue-Morse sequence, i.e., 
is the parity of the number of 1's in the binary representation of 
. It has approximate value
 |
(2)
|
(OEIS A055060). This constant is the smallest number 
for which there is a unique q-expansion
 |
(3)
|
(Komornik and Loreti 1998).
The constant 
is also the unique positive real root of
 |
(4)
|
(Finch 2003, p. 438).
Allouche and Cosnard (2000) showed that this constant is transcendental.
REFERENCES:
Allouche, J.-P. and Cosnard, M. "The Komornik-Loreti Constant Is Transcendental." Amer. Math. Monthly 107, 448-449, 2000.
Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 438-349, 2003.
Komornik, V. and Loreti, P. "Unique Developments in Non-Integer Bases." Amer. Math. Monthly 105, 636-639, 1998.
Sloane, N. J. A. Sequence A055060 in "The On-Line Encyclopedia of Integer Sequences."
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