A384281 Decimal expansion of the second smallest zero of the Laguerre polynomial of degree 4.

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

Offset

1,2

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

Example

1.74576110115834657568681671251794702367387451553107...

Mathematica

First[RealDigits[Root[LaguerreL[4, #] &, 2], 10, 100]] (* Paolo Xausa, Jun 05 2025 *)

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 |

4 | A384280, this sequence

Sequence in context: A357100 A085662 A379664 * A155684 A345292 A198357

Adjacent sequences: A384278 A384279 A384280 * A384282 A384283 A384284

Keyword

nonn,cons

Author

A.H.M. Smeets, May 26 2025

Status

approved