A384588 Decimal expansion of the weight factor for Laguerre-Gauss quadrature corresponding to abscissa A384586.

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

Offset

0,2

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

Example

0.038887908515005384272438168156209913722307191348276...

Mathematica

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

Prog

(PARI) solve(x = 0.1, 0.04, 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, A384586, A384587 | A384466, A384467, this sequence, A384589

Sequence in context: A157471 A288094 A131596 * A332892 A371137 A386411

Adjacent sequences: A384585 A384586 A384587 * A384589 A384590 A384591

Keyword

nonn,cons

Author

A.H.M. Smeets, Jun 07 2025

Status

approved