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 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