A384277 Decimal expansion of the smallest zero of the Laguerre polynomial of degree 3.

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

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 = 3.

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 3.

Formula

Smallest root of x^3 - 9 x^2 + 18 x - 6 = 0.

Example

0.41577455678347908331153387312827447354661741269311...

Mathematica

First[RealDigits[Root[LaguerreL[3, #] &, 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 | this sequence, A384278, A384279 | A384463, A384464, A384465

4 | A384280, A384281, A384586, A384587 | A384466, A384467, A384588, A384589

Sequence in context: A344026 A133866 A356045 * A242131 A177266 A356124

Adjacent sequences: A384274 A384275 A384276 * A384278 A384279 A384280

Keyword

nonn,cons

Author

A.H.M. Smeets, May 24 2025

Status

approved