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Decimal expansion of the largest positive zero of the Legendre polynomial of degree 7.
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%I #8 Apr 30 2024 02:25:46

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

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

%U 3,3,3,0,3,5,4,8,4,0,1,4,0,8,0,5,7,3,0

%N Decimal expansion of the largest positive zero of the Legendre polynomial of degree 7.

%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 429*x^6 - 693*x^4 + 315*x^2 - 35 = 0.

%e 0.949107912342758524526189684047851262400770937670617783548769...

%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