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

Author

A.H.M. Smeets, May 30 2025

Keywords

• nonn
• cons

Examples

			0.27851773356924084880144488845672648103489003098638...
		

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.

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

Programs

Mathematica

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

PARI

solve(x = 0.2, 0.3, 1944*x^3 - 1944*x^2 + 405*x - 4)

Formula

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