%I #8 Apr 30 2024 02:26:47

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

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

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

%N Decimal expansion of the largest positive zero of the Legendre polynomial of degree 6.

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

%H <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>.

%F Largest positive root of 231*x^6 - 315*x^4 + 105*x^2 - 5 = 0.

%e 0.932469514203152027812301554493994609134765737712289824872549...

%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