A384280 Decimal expansion of the smallest zero of the Laguerre polynomial of degree 4.

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

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 Polynomial.

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

Index entries for algebraic numbers, degree 4.

Formula

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

Example

0.32254768961939231180036145910436747974375722447429...

Mathematica

First[RealDigits[Root[LaguerreL[4, #] &, 1], 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 | this sequence, A384281

Sequence in context: A282161 A205675 A342331 * A375752 A058608 A112196

Adjacent sequences: A384277 A384278 A384279 * A384281 A384282 A384283

Keyword

nonn,cons

Author

A.H.M. Smeets, May 26 2025

Status

approved