A384467 Decimal expansion of the weight factor for Laguerre-Gauss quadrature corresponding to abscissa A384281.

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

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 = 4.

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 4.

Formula

Second largest root of 1990656*x^4 - 1990656*x^3 + 504576*x^2 - 16960*x + 9 = 0.

Example

0.35741869243779968664149201745809128176357836491934...

Mathematica

First[RealDigits[Root[1990656*#^4 - 1990656*#^3 + 504576*#^2 - 16960*# + 9 &, 3], 10, 100]] (* Paolo Xausa, Jun 26 2025 *)

Prog

(PARI) solve(x = 0.3, 0.4, 1990656*x^4 - 1990656*x^3 + 504576*x^2 - 16960*x + 9)

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, A384465

4 | A384280, A384281 | A384466, this sequence

Sequence in context: A204938 A101088 A134487 * A064537 A023899 A356026

Adjacent sequences: A384464 A384465 A384466 * A384468 A384469 A384470

Keyword

nonn,cons

Author

A.H.M. Smeets, May 30 2025

Status

approved