A384589 Decimal expansion of the weight factor for Laguerre-Gauss quadrature corresponding to abscissa A384587.

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

Offset

0,4

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

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

Example

0.00053929470556132745010379056762059321227725696643324...

Mathematica

First[RealDigits[Root[1990656*#^4 - 1990656*#^3 + 504576*#^2 - 16960*# + 9 &, 1], 10, 100, -1]] (* Paolo Xausa, Jun 26 2025 *)

Prog

(PARI) solve(x = 0.0, 0.01, 1990656*x^4 - 1990656*x^3 + 504576*x^2 - 16960*x + 9)

Crossrefs

Cf. A384590.

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, A384586, A384587 | A384466, A384467, A384588, this sequence

Sequence in context: A305327 A112812 A241624 * A159275 A374990 A059031

Adjacent sequences: A384586 A384587 A384588 * A384590 A384591 A384592

Keyword

nonn,cons

Author

A.H.M. Smeets, Jun 14 2025

Status

approved