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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A384279 #14 Jun 27 2025 01:02:23
%S A384279 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,
%T A384279 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,
%U A384279 4,4,5,2,8,7,2,5,9,2,0,2,3,8,4,7,9,6,1
%N A384279 Decimal expansion of the largest zero of the Laguerre polynomial of degree 3.
%H A384279 Paolo Xausa, <a href="/A384279/b384279.txt">Table of n, a(n) for n = 1..10000</a>
%H A384279 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. Table 25.9, n = 3.
%H A384279 A.H.M. Smeets, <a href="/A384277/a384277.txt">Abscissas and weight factors for Laguerre integration for some larger degrees</a>.
%H A384279 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>.
%H A384279 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Laguerre-GaussQuadrature.html">Laguerre-Gauss Quadrature</a>.
%H A384279 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>.
%F A384279 largest root of x^3 - 9 x^2 + 18 x - 6 = 0.
%e A384279 6.28994508293747919686641576551213165749352086624660...
%t A384279 First[RealDigits[Root[LaguerreL[3, #] &, 3], 10, 100]] (* _Paolo Xausa_, Jun 05 2025 *)
%Y A384279 Cf. A384590.
%Y A384279 There are k positive real zeros of the Laguerre polynomial of degree k:
%Y A384279    k | zeros                                    | corresponding weights for Laguerre-Gauss quadrature
%Y A384279   ---+------------------------------------------+-----------------------------------------------------
%Y A384279    2 | A101465, 1+A014176                       | A201488, A100954-3
%Y A384279    3 | A384277, A384278, this sequence          | A384463, A384464, A384465
%Y A384279    4 | A384280, A384281, A384586, A384587       | A384466, A384467, A384588, A384589
%K A384279 nonn,cons
%O A384279 1,1
%A A384279 _A.H.M. Smeets_, May 26 2025