cp's OEIS Frontend

A384281 Decimal expansion of the second smallest zero of the Laguerre polynomial of degree 4.

%I A384281 #10 Jun 05 2025 09:53:45
%S A384281 1,7,4,5,7,6,1,1,0,1,1,5,8,3,4,6,5,7,5,6,8,6,8,1,6,7,1,2,5,1,7,9,4,7,
%T A384281 0,2,3,6,7,3,8,7,4,5,1,5,5,3,1,0,7,2,5,0,1,7,8,2,7,8,2,6,6,0,9,9,8,4,
%U A384281 5,6,0,5,7,4,4,2,1,9,7,1,6,4,1,4,0,1,3
%N A384281 Decimal expansion of the second smallest zero of the Laguerre polynomial of degree 4.
%H A384281 Paolo Xausa, <a href="/A384281/b384281.txt">Table of n, a(n) for n = 1..10000</a>
%H A384281 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 A384281 A.H.M. Smeets, <a href="/A384277/a384277.txt">Abscissas and weight factors for Laguerre integration for some larger degrees</a>.
%H A384281 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>.
%H A384281 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Laguerre-GaussQuadrature.html">Laguerre-Gauss Quadrature</a>.
%H A384281 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A384281 Second smallest root of x^4 - 16 x^3 + 72 x^2 - 96 x + 24 = 0.
%e A384281 1.74576110115834657568681671251794702367387451553107...
%t A384281 First[RealDigits[Root[LaguerreL[4, #] &, 2], 10, 100]] (* _Paolo Xausa_, Jun 05 2025 *)
%Y A384281 There are k positive real zeros of the Laguerre polynomial of degree k:
%Y A384281    k | zeros                                    | corresponding weights for Laguerre-Gauss quadrature
%Y A384281   ---+------------------------------------------+-----------------------------------------------------
%Y A384281    2 | A101465, 1+A014176                       | A201488, A100954-3
%Y A384281    3 | A384277, A384278, A384279          |
%Y A384281    4 | A384280, this sequence
%K A384281 nonn,cons
%O A384281 1,2
%A A384281 _A.H.M. Smeets_, May 26 2025