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 A384586 #18 Aug 08 2025 11:56:54 %S A384586 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, %T A384586 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, %U A384586 2,8,4,5,0,8,7,5,1,4,3,1,5,8,9,7,6,5,3 %N A384586 Decimal expansion of the second largest zero of the Laguerre polynomial of degree 4. %H A384586 Paolo Xausa, <a href="/A384586/b384586.txt">Table of n, a(n) for n = 1..10000</a> %H A384586 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 A384586 V. I. Krylov, <a href="https://books.google.de/books?id=lswsAwAAQBAJ">Approximate calculation of integrals</a> (Dover publications) (1962) page 347 n=4. %H A384586 A.H.M. Smeets, <a href="/A384277/a384277.txt">Abscissas and weight factors for Laguerre integration for some larger degrees</a>. %H A384586 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>. %H A384586 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Laguerre-GaussQuadrature.html">Laguerre-Gauss Quadrature</a>. %H A384586 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>. %F A384586 Second largest root of x^4 - 16 x^3 + 72 x^2 - 96 x + 24 = 0. %e A384586 4.53662029692112798327928538495713788012578435338680... %t A384586 First[RealDigits[Root[LaguerreL[4, #] &, 3], 10, 100]] (* _Paolo Xausa_, Jun 18 2025 *) %o A384586 (PARI) solve(x = 2, 6, x^4 - 16*x^3 + 72*x^2 - 96*x + 24) %Y A384586 There are k positive real zeros of the Laguerre polynomial of degree k: %Y A384586 k | zeros | corresponding weights for Laguerre-Gauss quadrature %Y A384586 ---+------------------------------------------+----------------------------------------------------- %Y A384586 2 | A101465, 1+A014176 | A201488, A100954-3 %Y A384586 3 | A384277, A384278, A384279 | A384463, A384464, A384465 %Y A384586 4 | A384280, A384281, this sequence, A384587 | A384466, A384467, A384588, A384589 %K A384586 nonn,cons %O A384586 1,1 %A A384586 _A.H.M. Smeets_, Jun 04 2025