A384587 Decimal expansion of the largest zero of the Laguerre polynomial of degree 4.

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

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..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 Polynomial.

Eric Weisstein's World of Mathematics, Laguerre-Gauss Quadrature.

Index entries for algebraic numbers, degree 4.

Formula

Second largest root of x^4 - 16 x^3 + 72 x^2 - 96 x + 24 = 0.

Example

9.39507091230113312923353644342054761645658390660782...

Mathematica

First[RealDigits[Root[LaguerreL[4, #] &, 4], 10, 100]] (* Paolo Xausa, Jun 18 2025 *)

Prog

(PARI) solve(x = 6, 16, x^4 - 16*x^3 + 72*x^2 - 96*x + 24)

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, this sequence | A384466, A384467, A384588, A384589

Sequence in context: A198608 A273637 A086705 * A199866 A276558 A196829

Adjacent sequences: A384584 A384585 A384586 * A384588 A384589 A384590

Keyword

nonn,cons

Author

A.H.M. Smeets, Jun 07 2025

Status

approved