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 A384466 #20 Aug 08 2025 11:57:16 %S A384466 6,0,3,1,5,4,1,0,4,3,4,1,6,3,3,6,0,1,6,3,5,9,6,6,0,2,3,8,1,8,0,7,8,2, %T A384466 1,1,3,0,1,8,3,7,1,8,6,7,6,5,9,4,8,9,3,1,9,8,4,6,7,3,1,6,1,4,4,1,8,0, %U A384466 8,9,8,6,1,2,5,8,5,8,6,7,3,5,7,7,9,4,9 %N A384466 Decimal expansion of the weight factor for Laguerre-Gauss quadrature corresponding to abscissa A384280. %H A384466 Paolo Xausa, <a href="/A384466/b384466.txt">Table of n, a(n) for n = 0..10000</a> %H A384466 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 A384466 V. I. Krylov, <a href="https://books.google.de/books?id=lswsAwAAQBAJ">Approximate calculation of integrals</a> (Dover publications) (1962) page 347 n=4. %H A384466 A.H.M. Smeets, <a href="/A384277/a384277.txt">Abscissas and weight factors for Laguerre integration for some larger degrees</a>. %H A384466 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Laguerre-GaussQuadrature.html">Laguerre-Gauss Quadrature</a>. %H A384466 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>. %F A384466 Largest root of 1990656*x^4 - 1990656*x^3 + 504576*x^2 - 16960*x + 9 = 0. %e A384466 0.60315410434163360163596602381807821130183718676594... %t A384466 First[RealDigits[Root[1990656*#^4 - 1990656*#^3 + 504576*#^2 - 16960*# + 9 &, 4], 10, 100]] (* _Paolo Xausa_, Jun 26 2025 *) %o A384466 (PARI) solve(x = 0.6, 0.7, 1990656*x^4 - 1990656*x^3 + 504576*x^2 - 16960*x + 9) %Y A384466 There are k positive real zeros of the Laguerre polynomial of degree k: %Y A384466 k | zeros | corresponding weights for Laguerre-Gauss quadrature %Y A384466 ---+------------------------------------------+----------------------------------------------------- %Y A384466 2 | A101465, 1+A014176 | A201488, A100954-3 %Y A384466 3 | A384277, A384278, A384279 | A384463, A384464, A384465 %Y A384466 4 | A384280, A384281 | this sequence, A384467 %K A384466 nonn,cons %O A384466 0,1 %A A384466 _A.H.M. Smeets_, May 30 2025