A372270 - OEIS

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

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

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

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

%N Decimal expansion of the largest positive zero of the Legendre polynomial of degree 5.

%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 63*x^4 - 70*x^2 + 15 = 0.

%F Equals sqrt(5+2*sqrt(10/7))/3.

%e 0.906179845938663992797626878299392965125651910762530862873762...

%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