A309948 Decimal expansion of the real part of the square root of 1 + i.
1, 0, 9, 8, 6, 8, 4, 1, 1, 3, 4, 6, 7, 8, 0, 9, 9, 6, 6, 0, 3, 9, 8, 0, 1, 1, 9, 5, 2, 4, 0, 6, 7, 8, 3, 7, 8, 5, 4, 4, 3, 9, 3, 1, 2, 0, 9, 2, 7, 1, 5, 7, 7, 4, 3, 7, 4, 4, 4, 1, 1, 5, 7, 8, 8, 4, 2, 8, 7, 5, 0, 5, 3, 5, 5, 5, 2, 8, 4, 8, 1, 1, 1, 3, 6, 5, 3, 6, 0, 6, 6, 3, 5, 6, 4, 1
Offset: 1
Examples
Re(sqrt(1 + i)) = 1.09868411346780996603980119524...
Links
- Jean-Paul Allouche, Samin Riasat, and Jeffrey Shallit, More infinite products: Thue-Morse and the Gamma function, The Ramanujan Journal, Vol. 49 (2019), pp. 115-128; arXiv preprint, arXiv:1709.03398 [math.NT], 2017.
Programs
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Maple
Digits := 120: Im(-sqrt(-1 - I))*10^95: ListTools:-Reverse(convert(floor(%), base, 10)); # Peter Luschny, Sep 20 2019
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Mathematica
RealDigits[Sqrt[1/2 + 1/Sqrt[2]], 10, 100][[1]]
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PARI
real(sqrt(1+I)) \\ Michel Marcus, Sep 16 2019
Formula
Re(sqrt(1 + i)) = sqrt(1/2 + 1/sqrt(2)) = 2^(1/4) * cos(Pi/8).
Equals Im(-sqrt(-1 - i)). - Peter Luschny, Sep 20 2019
Equals Product_{k>=0} ((8*k+3)*(8*k+5)/((8*k+1)*(8*k+7)))^A010060(k) (Allouche et al., 2019). - Amiram Eldar, Feb 04 2024
Comments