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%I #8 Apr 30 2024 02:26:27
%S 5,3,8,4,6,9,3,1,0,1,0,5,6,8,3,0,9,1,0,3,6,3,1,4,4,2,0,7,0,0,2,0,8,8,
%T 0,4,9,6,7,2,8,6,6,0,6,9,0,5,5,5,9,9,5,6,2,0,2,2,3,1,6,2,7,0,5,9,4,7,
%U 1,1,8,5,3,6,7,7,5,5,2,9,1,0,3,5,8,0,3
%N Decimal expansion of the smallest 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 Smallest positive root of 63*x^4 - 70*x^2 + 15 = 0.
%F Equals sqrt(5-2*sqrt(10/7))/3.
%e 0.538469310105683091036314420700208804967286606905559956202231...
%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
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