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A372272 Decimal expansion of the middle positive zero of the Legendre polynomial of degree 6.

%I A372272 #14 Feb 27 2025 04:24:10
%S A372272 6,6,1,2,0,9,3,8,6,4,6,6,2,6,4,5,1,3,6,6,1,3,9,9,5,9,5,0,1,9,9,0,5,3,
%T A372272 4,7,0,0,6,4,4,8,5,6,4,3,9,5,1,7,0,0,7,0,8,1,4,5,2,6,7,0,5,8,5,2,1,8,
%U A372272 3,4,9,6,6,0,7,1,4,3,1,0,0,9,4,4,2,8,6
%N A372272 Decimal expansion of the middle positive zero of the Legendre polynomial of degree 6.
%H A372272 Paolo Xausa, <a href="/A372272/b372272.txt">Table of n, a(n) for n = 0..10000</a>
%H A372272 Wikipedia, <a href="https://en.wikipedia.org/wiki/Legendre_polynomials">Legendre polynomials</a>.
%H A372272 <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>.
%F A372272 Middle positive root of 231*x^6 - 315*x^4 + 105*x^2 - 5 = 0.
%e A372272 0.661209386466264513661399595019905347006448564395170070814526...
%t A372272 First[RealDigits[Root[LegendreP[6, #] &, 5], 10, 100]] (* _Paolo Xausa_, Feb 27 2025 *)
%Y A372272 Cf. A008316, A100258.
%Y A372272 There are floor(k/2) positive zeros of the Legendre polynomial of degree k:
%Y A372272    k | zeros
%Y A372272   ---+--------------------------
%Y A372272    2 | A020760
%Y A372272    3 | A010513/10
%Y A372272    4 | A372267, A372268
%Y A372272    5 | A372269, A372270
%Y A372272    6 | A372271, A372272, A372273
%Y A372272    7 | A372274, A372275, A372276
%K A372272 nonn,cons
%O A372272 0,1
%A A372272 _Pontus von Brömssen_, Apr 25 2024