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 A384464 #12 Jun 26 2025 07:39:36 %S A384464 2,7,8,5,1,7,7,3,3,5,6,9,2,4,0,8,4,8,8,0,1,4,4,4,8,8,8,4,5,6,7,2,6,4, %T A384464 8,1,0,3,4,8,9,0,0,3,0,9,8,6,3,8,8,6,7,1,8,5,6,7,3,4,9,4,8,4,3,4,4,9, %U A384464 4,0,9,6,5,7,9,3,6,5,7,5,3,0,3,5,7,4,2 %N A384464 Decimal expansion of the weight factor for Laguerre-Gauss quadrature corresponding to abscissa A384278. %H A384464 Paolo Xausa, <a href="/A384464/b384464.txt">Table of n, a(n) for n = 0..10000</a> %H A384464 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 A384464 A.H.M. Smeets, <a href="/A384277/a384277.txt">Abscissas and weight factors for Laguerre integration for some larger degrees</a>. %H A384464 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Laguerre-GaussQuadrature.html">Laguerre-Gauss Quadrature</a>. %H A384464 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>. %F A384464 Second largest root of 1944*x^3 - 1944*x^2 + 405*x - 4 = 0. %e A384464 0.27851773356924084880144488845672648103489003098638... %t A384464 First[RealDigits[Root[1944*#^3 - 1944*#^2 + 405*# - 4 &, 2], 10, 100]] (* _Paolo Xausa_, Jun 26 2025 *) %o A384464 (PARI) solve(x = 0.2, 0.3, 1944*x^3 - 1944*x^2 + 405*x - 4) %Y A384464 There are k positive real zeros of the Laguerre polynomial of degree k: %Y A384464 k | zeros | corresponding weights for Laguerre-Gauss quadrature %Y A384464 ---+------------------------------------------+----------------------------------------------------- %Y A384464 2 | A101465, 1+A014176 | A201488, A100954-3 %Y A384464 3 | A384277, A384278, A384279 | A384463, this sequence, A384465 %Y A384464 4 | A384280, A384281 | A384466, A384467 %K A384464 nonn,cons %O A384464 0,1 %A A384464 _A.H.M. Smeets_, May 30 2025