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 A384467 #14 Jun 26 2025 07:37:37 %S A384467 3,5,7,4,1,8,6,9,2,4,3,7,7,9,9,6,8,6,6,4,1,4,9,2,0,1,7,4,5,8,0,9,1,2, %T A384467 8,1,7,6,3,5,7,8,3,6,4,9,1,9,3,4,0,9,2,1,7,4,8,2,2,5,0,4,6,6,7,5,7,6, %U A384467 4,1,5,9,2,0,7,0,2,7,1,1,5,1,4,3,6,2,8 %N A384467 Decimal expansion of the weight factor for Laguerre-Gauss quadrature corresponding to abscissa A384281. %H A384467 Paolo Xausa, <a href="/A384467/b384467.txt">Table of n, a(n) for n = 0..10000</a> %H A384467 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 A384467 A.H.M. Smeets, <a href="/A384277/a384277.txt">Abscissas and weight factors for Laguerre integration for some larger degrees</a>. %H A384467 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Laguerre-GaussQuadrature.html">Laguerre-Gauss Quadrature</a>. %H A384467 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>. %F A384467 Second largest root of 1990656*x^4 - 1990656*x^3 + 504576*x^2 - 16960*x + 9 = 0. %e A384467 0.35741869243779968664149201745809128176357836491934... %t A384467 First[RealDigits[Root[1990656*#^4 - 1990656*#^3 + 504576*#^2 - 16960*# + 9 &, 3], 10, 100]] (* _Paolo Xausa_, Jun 26 2025 *) %o A384467 (PARI) solve(x = 0.3, 0.4, 1990656*x^4 - 1990656*x^3 + 504576*x^2 - 16960*x + 9) %Y A384467 There are k positive real zeros of the Laguerre polynomial of degree k: %Y A384467 k | zeros | corresponding weights for Laguerre-Gauss quadrature %Y A384467 ---+------------------------------------------+----------------------------------------------------- %Y A384467 2 | A101465, 1+A014176 | A201488, A100954-3 %Y A384467 3 | A384277, A384278, A384279 | A384463, A384464, A384465 %Y A384467 4 | A384280, A384281 | A384466, this sequence %K A384467 nonn,cons %O A384467 0,1 %A A384467 _A.H.M. Smeets_, May 30 2025