[seqfan] Re: Is A086744 known to be irrational?

jp allouche jean-paul.allouche at imj-prg.fr
Sun Apr 15 09:15:32 CEST 2018


Hi

No the arithmetic nature of this constant is not known.
It is probably transcendental but it is not even known that
it is irrational; its study might involve e^{-\gamma} where
\gamma is the Euler constant: see, e.g., Section 3.3 and the references
in http://jtnb.cedram.org/cedram-bin/article/JTNB_2015__27_2_375_0.pdf
where this constant is compared with a "similar" constant with value 
\sqrt{2}/2

best
jean-paul


Le 14/04/2018 à 21:46, Vladimir Reshetnikov a écrit :
> Dear SeqFans,
>
> https://oeis.org/A086744 gives a decimal expansion of the constant
> 1.6281601297189... that results from an infinite product involving the
> Thue–Morse sequence. There is a comment for the sequence: "It is an
> open problem to decide if this number is algebraic." I wonder if this
> constant is already known to be irrational?
>
> --
> Thanks
> Vladimir
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/




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