A393356 Decimal expansion of the weight factor for Hermite-Gauss quadrature corresponding to abscissa A393354.

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

Offset

0,2

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, this sequence

Links

Paolo Xausa, Table of n, a(n) for n = 0..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 transcendental numbers.

Formula

This constant divided by sqrt(Pi) is a root of 48*x^2 - 24*x + 1 = 0.

Equals sqrt(Pi)*(3-sqrt(6))/12.

Example

0.0813128354472451771430345571898884117633329166383...

Mathematica

First[RealDigits[Sqrt[Pi]*(3 - Sqrt[6])/12, 10, 100, -1]] (* Paolo Xausa, Feb 19 2026 *)

Prog

(PARI) sqrt(Pi)*polrootsreal(Pol([48, -24, 1]))[1]
(PARI) sqrt(Pi)*(3-sqrt(6))/12

Crossrefs

Cf. A393354.

Sequence in context: A266152 A021127 A379469 * A010155 A386590 A019607

Adjacent sequences: A393353 A393354 A393355 * A393357 A393358 A393359

Keyword

nonn,cons

Author

A.H.M. Smeets, Feb 12 2026

Status

approved