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 A384277 #16 Jun 27 2025 01:02:12 %S A384277 4,1,5,7,7,4,5,5,6,7,8,3,4,7,9,0,8,3,3,1,1,5,3,3,8,7,3,1,2,8,2,7,4,4, %T A384277 7,3,5,4,6,6,1,7,4,1,2,6,9,3,1,1,8,4,6,5,0,9,3,9,6,5,9,5,4,3,2,2,3,2, %U A384277 5,0,1,9,9,3,6,9,1,3,3,1,4,9,5,7,1,9,6 %N A384277 Decimal expansion of the smallest zero of the Laguerre polynomial of degree 3. %H A384277 Paolo Xausa, <a href="/A384277/b384277.txt">Table of n, a(n) for n = 0..10000</a> %H A384277 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 A384277 A.H.M. Smeets, <a href="/A384277/a384277.txt">Abscissas and weight factors for Laguerre integration for some larger degrees</a>. %H A384277 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>. %H A384277 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Laguerre-GaussQuadrature.html">Laguerre-Gauss Quadrature</a>. %H A384277 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>. %F A384277 Smallest root of x^3 - 9 x^2 + 18 x - 6 = 0. %e A384277 0.41577455678347908331153387312827447354661741269311... %t A384277 First[RealDigits[Root[LaguerreL[3, #] &, 1], 10, 100]] (* _Paolo Xausa_, Jun 05 2025 *) %Y A384277 There are k positive real zeros of the Laguerre polynomial of degree k: %Y A384277 k | zeros | corresponding weights for Laguerre-Gauss quadrature %Y A384277 ---+------------------------------------------+----------------------------------------------------- %Y A384277 2 | A101465, 1+A014176 | A201488, A100954-3 %Y A384277 3 | this sequence, A384278, A384279 | A384463, A384464, A384465 %Y A384277 4 | A384280, A384281, A384586, A384587 | A384466, A384467, A384588, A384589 %K A384277 nonn,cons %O A384277 0,1 %A A384277 _A.H.M. Smeets_, May 24 2025