cp's OEIS Frontend

A372271 Decimal expansion of the smallest positive zero of the Legendre polynomial of degree 6.

%I A372271 #14 Feb 27 2025 04:25:17
%S A372271 2,3,8,6,1,9,1,8,6,0,8,3,1,9,6,9,0,8,6,3,0,5,0,1,7,2,1,6,8,0,7,1,1,9,
%T A372271 3,5,4,1,8,6,1,0,6,3,0,1,4,0,0,2,1,3,5,0,1,8,1,3,9,5,1,6,4,5,7,4,2,7,
%U A372271 4,9,3,4,2,7,5,6,3,9,8,4,2,2,4,9,2,2,4
%N A372271 Decimal expansion of the smallest positive zero of the Legendre polynomial of degree 6.
%H A372271 Paolo Xausa, <a href="/A372271/b372271.txt">Table of n, a(n) for n = 0..10000</a>
%H A372271 Wikipedia, <a href="https://en.wikipedia.org/wiki/Legendre_polynomials">Legendre polynomials</a>.
%H A372271 <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>.
%F A372271 Smallest positive root of 231*x^6 - 315*x^4 + 105*x^2 - 5 = 0.
%e A372271 0.238619186083196908630501721680711935418610630140021350181395...
%t A372271 First[RealDigits[Root[LegendreP[6, #] &, 4], 10, 100]] (* _Paolo Xausa_, Feb 27 2025 *)
%Y A372271 Cf. A008316, A100258.
%Y A372271 There are floor(k/2) positive zeros of the Legendre polynomial of degree k:
%Y A372271    k | zeros
%Y A372271   ---+--------------------------
%Y A372271    2 | A020760
%Y A372271    3 | A010513/10
%Y A372271    4 | A372267, A372268
%Y A372271    5 | A372269, A372270
%Y A372271    6 | A372271, A372272, A372273
%Y A372271    7 | A372274, A372275, A372276
%K A372271 nonn,cons
%O A372271 0,1
%A A372271 _Pontus von Brömssen_, Apr 25 2024