A393364 - OEIS

%I #11 Jun 05 2026 16:20:05

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

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

%U 2,2,6,6,3,7,3,3,1,6,4,0,4,1,2,1,5,3,8,6

%N Decimal expansion of the largest positive zero of the Hermite polynomial of degree 6.

%C There are floor(k/2) positive zeros of the Hermite polynomial of degree k:

%C    k | zeros                           | corresponding weights for Hermite-Gauss quadrature

%C   ---+---------------------------------+----------------------------------------------------

%C    2 | A010503                         | A019704

%C    3 | 0, A115754                      | 10*A019717, A019708

%C    4 | A393353, A393354                | A393355, A393356

%C    5 | 0, A393357, A393358             | A245887, A393360, A393361

%C    6 | A393362, A393363, this sequence | A393365, A393366, A393367

%H A.H.M. Smeets, <a href="/A393364/b393364.txt">Table of n, a(n) for n = 1..10000</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. Eq. 25.4.46 p. 890 and Table 25.10 p. 924.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Hermite-GaussQuadrature.html">Hermite-Gauss Quadrature</a>.

%H <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>.

%e 2.35060497367449222283392198706092084653786382729409...

%t RealDigits[x /. FindRoot[HermiteH[6, x], {x, 2}, WorkingPrecision -> 100]][[1]] (* _Amiram Eldar_, Feb 24 2026 *)

%o (PARI) polrootsreal(polhermite(6))[6]

%K nonn,cons

%O 1,1

%A _A.H.M. Smeets_, Feb 24 2026