OFFSET
1,3
COMMENTS
i is the imaginary unit such that i^2 = -1.
Also imaginary part of sqrt(-1 + i).
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.
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
EXAMPLE
Re(sqrt(1 + i)) = 1.09868411346780996603980119524...
MAPLE
Digits := 120: Im(-sqrt(-1 - I))*10^95:
ListTools:-Reverse(convert(floor(%), base, 10)); # Peter Luschny, Sep 20 2019
MATHEMATICA
RealDigits[Sqrt[1/2 + 1/Sqrt[2]], 10, 100][[1]]
PROG
(PARI) real(sqrt(1+I)) \\ Michel Marcus, Sep 16 2019
CROSSREFS
KEYWORD
AUTHOR
Alonso del Arte, Aug 24 2019
STATUS
approved