A384586 Decimal expansion of the second largest zero of the Laguerre polynomial of degree 4.
4, 5, 3, 6, 6, 2, 0, 2, 9, 6, 9, 2, 1, 1, 2, 7, 9, 8, 3, 2, 7, 9, 2, 8, 5, 3, 8, 4, 9, 5, 7, 1, 3, 7, 8, 8, 0, 1, 2, 5, 7, 8, 4, 3, 5, 3, 3, 8, 6, 8, 0, 4, 6, 4, 9, 7, 4, 8, 0, 5, 7, 5, 8, 7, 5, 5, 5, 8, 2, 8, 4, 5, 0, 8, 7, 5, 1, 4, 3, 1, 5, 8, 9, 7, 6, 5, 3
Offset: 1
Examples
4.53662029692112798327928538495713788012578435338680...
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.
- V. I. Krylov, Approximate calculation of integrals (Dover publications) (1962) page 347 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.
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[4, #] &, 3], 10, 100]] (* Paolo Xausa, Jun 18 2025 *)
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PARI
solve(x = 2, 6, x^4 - 16*x^3 + 72*x^2 - 96*x + 24)
Formula
Second largest root of x^4 - 16 x^3 + 72 x^2 - 96 x + 24 = 0.