|
%I #8 Apr 30 2024 02:26:53
%S 7,4,1,5,3,1,1,8,5,5,9,9,3,9,4,4,3,9,8,6,3,8,6,4,7,7,3,2,8,0,7,8,8,4,
%T 0,7,0,7,4,1,4,7,6,4,7,1,4,1,3,9,0,2,6,0,1,1,9,9,5,5,3,5,1,9,6,7,4,2,
%U 9,8,7,4,6,7,2,1,8,0,5,1,3,7,9,2,8,2,6
%N Decimal expansion of the middle 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 Middle positive root of 429*x^6 - 693*x^4 + 315*x^2 - 35 = 0.
%e 0.741531185599394439863864773280788407074147647141390260119955...
%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
|
