A309949 - OEIS

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A309949

Decimal expansion of the imaginary part of the square root of 1 + i.

4, 5, 5, 0, 8, 9, 8, 6, 0, 5, 6, 2, 2, 2, 7, 3, 4, 1, 3, 0, 4, 3, 5, 7, 7, 5, 7, 8, 2, 2, 4, 6, 8, 5, 6, 9, 6, 2, 0, 1, 9, 0, 3, 7, 8, 4, 8, 3, 1, 5, 0, 0, 9, 2, 5, 8, 8, 2, 5, 9, 5, 6, 9, 4, 9, 0, 8, 0, 0, 2, 0, 3, 2, 3, 3, 4, 4, 8, 2, 9, 1, 5, 9, 1, 4, 0, 1, 8, 1, 9, 7, 6, 1, 0, 2

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

i is the imaginary unit such that i^2 = -1.

Multiplied by -1, this is the imaginary part of the square root of 1 - i. And also the real part of -sqrt(1 + i) - i + sqrt(1 + i)^3, which is a unit in Q(sqrt(1 + i)).

LINKS

Table of n, a(n) for n=0..94.

FORMULA

Equals sqrt(1/sqrt(2) - 1/2) = 2^(1/4) * sin(Pi/8).

Equals sqrt((sqrt(2) - 1)/2) = A010767 * A182168. - Bernard Schott, Sep 16 2019

Equals Re(sqrt(-1 - i)). - Peter Luschny, Sep 20 2019

Equals Product_{k>=0} ((8*k - 1)*(8*k + 4))/((8*k - 2)*(8*k + 5)). - Antonio Graciá Llorente, Feb 24 2024

EXAMPLE

Im(sqrt(1 + i)) = 0.45508986056222734130435775782247...

MAPLE

Digits := 120: Re(sqrt(-1 - I))*10^95:

ListTools:-Reverse(convert(floor(%), base, 10)); # Peter Luschny, Sep 20 2019