A372268 - OEIS

%I #8 Apr 30 2024 02:26:23

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

%T 0,5,0,9,5,7,2,5,3,7,9,6,2,9,7,1,7,6,3,7,6,1,5,7,2,1,9,2,0,9,0,6,5,2,

%U 9,4,7,1,4,9,5,0,4,8,8,6,5,7,0,4,1,6,2

%N Decimal expansion of the largest positive zero of the Legendre polynomial of degree 4.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Legendre_polynomials">Legendre polynomials</a>.

%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.

%F Largest positive root of 35*x^4 - 30*x^2 + 3 = 0.

%F Equals sqrt((3+2*sqrt(6/5))/7).

%e 0.861136311594052575223946488892809505095725379629717637615721...

%Y Cf. A008316, A100258.

%Y There are floor(k/2) positive zeros of the Legendre polynomial of degree k:

%Y    k | zeros

%Y   ---+--------------------------

%Y    2 | A020760

%Y    3 | A010513/10

%Y    4 | A372267, A372268

%Y    5 | A372269, A372270

%Y    6 | A372271, A372272, A372273

%Y    7 | A372274, A372275, A372276

%K nonn,cons

%O 0,1

%A _Pontus von Brömssen_, Apr 25 2024