A384464 Decimal expansion of the weight factor for Laguerre-Gauss quadrature corresponding to abscissa A384278.

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

Offset

0,1

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]. 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

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

Example

0.27851773356924084880144488845672648103489003098638...

Mathematica

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

Prog

(PARI) solve(x = 0.2, 0.3, 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, this sequence, A384465

4 | A384280, A384281 | A384466, A384467

Sequence in context: A360441 A019731 A363438 * A021363 A352495 A141721

Adjacent sequences: A384461 A384462 A384463 * A384465 A384466 A384467

Keyword

nonn,cons

Author

A.H.M. Smeets, May 30 2025

Status

approved