A393374 Decimal expansion of the weight factor for Hermite-Gauss quadrature of degree 7 corresponding to abscissa A393370.

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

Offset

0,4

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, A393364 | A393365, A393366, A393367

7 | 0, A393368, A393369, A393370 | A393371, A393372, A393373, this sequence

Links

Table of n, a(n) for n=0..90.

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 1234800*x^3 -335160*x^2 + 9303*x - 5 = 0 (see also A393904).

Example

0.00097178124509951915414942425593895964444240121701...

Mathematica

RealDigits[Sqrt[Pi] * Root[1234800*x^3 - 335160*x^2 + 9303*x - 5, 1], 10, 100, -1][[1]] (* Amiram Eldar, Mar 07 2026 *)

Prog

(PARI) sqrt(Pi)*polrootsreal(Pol([1234800, -335160, 9303, -5]))[1]

Crossrefs

Cf. A393370, A393904.

Sequence in context: A383860 A393891 A254249 * A298752 A154396 A380795

Adjacent sequences: A393371 A393372 A393373 * A393375 A393376 A393377

Keyword

nonn,cons

Author

A.H.M. Smeets, Mar 07 2026

Status

approved