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 A384278 #13 Jun 27 2025 01:02:17 %S A384278 2,2,9,4,2,8,0,3,6,0,2,7,9,0,4,1,7,1,9,8,2,2,0,5,0,3,6,1,3,5,9,5,9,3, %T A384278 8,6,8,9,5,9,8,6,1,7,2,1,0,6,0,2,8,0,8,3,4,0,3,5,2,0,1,2,4,8,0,8,4,0, %U A384278 3,0,4,5,1,3,3,7,1,6,6,4,4,6,5,6,3,1,8 %N A384278 Decimal expansion of the second smallest zero of the Laguerre polynomial of degree 3. %H A384278 Paolo Xausa, <a href="/A384278/b384278.txt">Table of n, a(n) for n = 1..10000</a> %H A384278 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 A384278 A.H.M. Smeets, <a href="/A384277/a384277.txt">Abscissas and weight factors for Laguerre integration for some larger degrees</a>. %H A384278 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>. %H A384278 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Laguerre-GaussQuadrature.html">Laguerre-Gauss Quadrature</a>. %H A384278 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>. %F A384278 Second smallest root of x^3 - 9 x^2 + 18 x - 6 = 0. %e A384278 2.29428036027904171982205036135959386895986172106028... %t A384278 First[RealDigits[Root[LaguerreL[3, #] &, 2], 10, 100]] (* _Paolo Xausa_, Jun 05 2025 *) %Y A384278 There are k positive real zeros of the Laguerre polynomial of degree k: %Y A384278 k | zeros | corresponding weights for Laguerre-Gauss quadrature %Y A384278 ---+------------------------------------------+----------------------------------------------------- %Y A384278 2 | A101465, 1+A014176 | A201488, A100954-3 %Y A384278 3 | A384277, this sequence, A384279 | A384463, A384464, A384465 %Y A384278 4 | A384280, A384281, A384586, A384587 | A384466, A384467, A384588, A384589 %K A384278 nonn,cons %O A384278 1,1 %A A384278 _A.H.M. Smeets_, May 24 2025