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A372273 Decimal expansion of the largest positive zero of the Legendre polynomial of degree 6.

%I A372273 #13 Feb 27 2025 05:04:57
%S A372273 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 A372273 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 A372273 3,5,0,0,8,4,4,2,0,0,1,9,6,2,7,6,2,8,8
%N A372273 Decimal expansion of the largest positive zero of the Legendre polynomial of degree 6.
%H A372273 Paolo Xausa, <a href="/A372273/b372273.txt">Table of n, a(n) for n = 0..10000</a>
%H A372273 Wikipedia, <a href="https://en.wikipedia.org/wiki/Legendre_polynomials">Legendre polynomials</a>.
%H A372273 <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>.
%F A372273 Largest positive root of 231*x^6 - 315*x^4 + 105*x^2 - 5 = 0.
%e A372273 0.932469514203152027812301554493994609134765737712289824872549...
%t A372273 First[RealDigits[Root[LegendreP[6, #] &, 6], 10, 100]] (* _Paolo Xausa_, Feb 27 2025 *)
%Y A372273 Cf. A008316, A100258.
%Y A372273 There are floor(k/2) positive zeros of the Legendre polynomial of degree k:
%Y A372273    k | zeros
%Y A372273   ---+--------------------------
%Y A372273    2 | A020760
%Y A372273    3 | A010513/10
%Y A372273    4 | A372267, A372268
%Y A372273    5 | A372269, A372270
%Y A372273    6 | A372271, A372272, A372273
%Y A372273    7 | A372274, A372275, A372276
%K A372273 nonn,cons
%O A372273 0,1
%A A372273 _Pontus von Brömssen_, Apr 25 2024