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
Examples
0.41577455678347908331153387312827447354661741269311...
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.
Crossrefs
There are k positive real zeros of the Laguerre polynomial of degree k:
k | zeros | corresponding weights for Laguerre-Gauss quadrature
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Programs
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Mathematica
First[RealDigits[Root[LaguerreL[3, #] &, 1], 10, 100]] (* Paolo Xausa, Jun 05 2025 *)
Formula
Smallest root of x^3 - 9 x^2 + 18 x - 6 = 0.