A384465 Decimal expansion of the weight factor for Laguerre-Gauss quadrature corresponding to abscissa A384279.

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

Offset

-1,3

Links

Paolo Xausa, 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]. Table 25.9, n = 3.

A.H.M. Smeets, Abscissas and weight factors for Laguerre integration for some larger degrees.

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

Index entries for algebraic numbers, degree 3.

Formula

Smallest root of 1944*x^3 - 1944*x^2 + 405*x - 4 = 0.

Example

0.010389256501586135748964920400679087655716172724057...

Mathematica

First[RealDigits[Root[1944*#^3 - 1944*#^2 + 405*# - 4 &, 1], 10, 100]] (* Paolo Xausa, Jun 26 2025 *)

Prog

(PARI) solve(x = 0, 0.1, 1944*x^3 - 1944*x^2 + 405*x - 4)

Crossrefs

There are k positive real zeros of the Laguerre polynomial of degree k:

k | zeros | corresponding weights for Laguerre-Gauss quadrature

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

2 | A101465, 1+A014176 | A201488, A100954-3

3 | A384277, A384278, A384279 | A384463, A384464, this sequence

4 | A384280, A384281 | A384466, A384467

Sequence in context: A245263 A016672 A177272 * A010630 A197811 A277827

Adjacent sequences: A384462 A384463 A384464 * A384466 A384467 A384468

Keyword

nonn,cons

Author

A.H.M. Smeets, May 30 2025

Status

approved