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A384280 Decimal expansion of the smallest zero of the Laguerre polynomial of degree 4.

%I A384280 #11 Jun 05 2025 08:18:05
%S A384280 3,2,2,5,4,7,6,8,9,6,1,9,3,9,2,3,1,1,8,0,0,3,6,1,4,5,9,1,0,4,3,6,7,4,
%T A384280 7,9,7,4,3,7,5,7,2,2,4,4,7,4,2,9,5,7,6,7,1,8,8,4,5,1,8,5,3,8,0,6,9,6,
%U A384280 8,6,7,8,7,0,7,7,0,4,0,0,9,8,6,8,5,8,5
%N A384280 Decimal expansion of the smallest zero of the Laguerre polynomial of degree 4.
%H A384280 Paolo Xausa, <a href="/A384280/b384280.txt">Table of n, a(n) for n = 0..10000</a>
%H A384280 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 = 4.
%H A384280 A.H.M. Smeets, <a href="/A384277/a384277.txt">Abscissas and weight factors for Laguerre integration for some larger degrees</a>.
%H A384280 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>.
%H A384280 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Laguerre-GaussQuadrature.html">Laguerre-Gauss Quadrature</a>.
%H A384280 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A384280 Smallest root of x^4 - 16 x^3 + 72 x^2 - 96 x + 24 = 0.
%e A384280 0.32254768961939231180036145910436747974375722447429...
%t A384280 First[RealDigits[Root[LaguerreL[4, #] &, 1], 10, 100]] (* _Paolo Xausa_, Jun 05 2025 *)
%Y A384280 There are k positive real zeros of the Laguerre polynomial of degree k:
%Y A384280    k | zeros                                    | corresponding weights for Laguerre-Gauss quadrature
%Y A384280   ---+------------------------------------------+-----------------------------------------------------
%Y A384280    2 | A101465, 1+A014176                       | A201488, A100954-3
%Y A384280    3 | A384277, A384278, A384279          |
%Y A384280    4 | this sequence, A384281
%K A384280 nonn,cons
%O A384280 0,1
%A A384280 _A.H.M. Smeets_, May 26 2025