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.
%I A384587 #11 Jun 18 2025 12:23:13 %S A384587 9,3,9,5,0,7,0,9,1,2,3,0,1,1,3,3,1,2,9,2,3,3,5,3,6,4,4,3,4,2,0,5,4,7, %T A384587 6,1,6,4,5,6,5,8,3,9,0,6,6,0,7,8,2,7,0,8,1,2,8,0,7,0,7,8,9,7,6,3,8,7, %U A384587 4,6,8,1,2,9,7,4,9,5,5,6,6,7,0,1,4,7,4 %N A384587 Decimal expansion of the largest zero of the Laguerre polynomial of degree 4. %H A384587 Paolo Xausa, <a href="/A384587/b384587.txt">Table of n, a(n) for n = 1..10000</a> %H A384587 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 A384587 A.H.M. Smeets, <a href="/A384277/a384277.txt">Abscissas and weight factors for Laguerre integration for some larger degrees</a>. %H A384587 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>. %H A384587 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Laguerre-GaussQuadrature.html">Laguerre-Gauss Quadrature</a>. %H A384587 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>. %F A384587 Second largest root of x^4 - 16 x^3 + 72 x^2 - 96 x + 24 = 0. %e A384587 9.39507091230113312923353644342054761645658390660782... %t A384587 First[RealDigits[Root[LaguerreL[4, #] &, 4], 10, 100]] (* _Paolo Xausa_, Jun 18 2025 *) %o A384587 (PARI) solve(x = 6, 16, x^4 - 16*x^3 + 72*x^2 - 96*x + 24) %Y A384587 There are k positive real zeros of the Laguerre polynomial of degree k: %Y A384587 k | zeros | corresponding weights for Laguerre-Gauss quadrature %Y A384587 ---+------------------------------------------+----------------------------------------------------- %Y A384587 2 | A101465, 1+A014176 | A201488, A100954-3 %Y A384587 3 | A384277, A384278, A384279 | A384463, A384464, A384465 %Y A384587 4 | A384280, A384281, A384586, this sequence | A384466, A384467, A384588, A384589 %K A384587 nonn,cons %O A384587 1,1 %A A384587 _A.H.M. Smeets_, Jun 07 2025