A393364 Decimal expansion of the largest positive zero of the Hermite polynomial of degree 6.

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

Offset

1,1

Comments

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

k | zeros | corresponding weights for Hermite-Gauss quadrature

---+---------------------------------+----------------------------------------------------

2 | A010503 | A019704

3 | 0, A115754 | 10*A019717, A019708

4 | A393353, A393354 | A393355, A393356

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

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

Links

A.H.M. Smeets, Table of n, a(n) for n = 1..10000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 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.

Eric Weisstein's World of Mathematics, Hermite-Gauss Quadrature.

Index entries for algebraic numbers, degree 6.

Example

2.35060497367449222283392198706092084653786382729409...

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A082118 A079344 A096535 * A126047 A023049 A240979

Adjacent sequences: A393361 A393362 A393363 * A393365 A393366 A393367

Keyword

nonn,cons

Author

A.H.M. Smeets, Feb 24 2026

Status

approved