A384279 Decimal expansion of the largest zero of the Laguerre polynomial of degree 3.

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

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 = 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

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

Example

6.28994508293747919686641576551213165749352086624660...

Mathematica

First[RealDigits[Root[LaguerreL[3, #] &, 3], 10, 100]] (* Paolo Xausa, Jun 05 2025 *)

Crossrefs

Cf. A384590.

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, this sequence | A384463, A384464, A384465

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

Sequence in context: A378713 A021163 A114866 * A248270 A201324 A107826

Adjacent sequences: A384276 A384277 A384278 * A384280 A384281 A384282

Keyword

nonn,cons

Author

A.H.M. Smeets, May 26 2025

Status

approved