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 A384463 #12 Jun 26 2025 07:40:02 %S A384463 7,1,1,0,9,3,0,0,9,9,2,9,1,7,3,0,1,5,4,4,9,5,9,0,1,9,1,1,4,2,5,9,4,4, %T A384463 3,1,3,0,9,3,9,3,7,9,6,2,8,9,5,5,3,4,4,5,1,3,1,7,1,7,2,4,4,3,6,1,9,0, %U A384463 2,1,5,5,1,2,2,1,3,2,2,3,5,8,2,0,3,7,2 %N A384463 Decimal expansion of the weight factor for Laguerre-Gauss quadrature corresponding to abscissa A384277. %H A384463 Paolo Xausa, <a href="/A384463/b384463.txt">Table of n, a(n) for n = 0..10000</a> %H A384463 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 A384463 A.H.M. Smeets, <a href="/A384277/a384277.txt">Abscissas and weight factors for Laguerre integration for some larger degrees</a>. %H A384463 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Laguerre-GaussQuadrature.html">Laguerre-Gauss Quadrature</a>. %H A384463 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>. %F A384463 Largest root of 1944*x^3 - 1944*x^2 + 405*x - 4 = 0. %e A384463 0.71109300992917301544959019114259443130939379628955... %t A384463 First[RealDigits[Root[1944*#^3 - 1944*#^2 + 405*# - 4 &, 3], 10, 100]] (* _Paolo Xausa_, Jun 26 2025 *) %o A384463 (PARI) solve(x = 0.7, 0.8, 1944*x^3 - 1944*x^2 + 405*x - 4) %Y A384463 There are k positive real zeros of the Laguerre polynomial of degree k: %Y A384463 k | zeros | corresponding weights for Laguerre-Gauss quadrature %Y A384463 ---+------------------------------------------+----------------------------------------------------- %Y A384463 2 | A101465, 1+A014176 | A201488, A100954-3 %Y A384463 3 | A384277, A384278, A384279 | this sequence, A384464, A384465 %Y A384463 4 | A384280, A384281 | A384466, A384467 %K A384463 nonn,cons %O A384463 0,1 %A A384463 _A.H.M. Smeets_, May 30 2025