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 A382688 #8 Apr 24 2025 16:41:17 %S A382688 3,8,1,8,3,0,0,5,0,5,0,5,1,1,8,9,4,4,9,5,0,3,6,9,7,7,5,4,8,8,9,7,5,1, %T A382688 3,3,8,7,8,3,6,5,0,8,3,5,3,3,8,6,2,7,3,4,7,5,1,0,8,3,4,5,1,0,3,0,7,0, %U A382688 5,5,4,6,4,3,4,1,2,9,7,0,8,3,4 %N A382688 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372274. %C A382688 There are floor(k/2) positive zeros of the Legendre polynomial of degree k: %C A382688 k | zeros | corresponding weights %C A382688 ---+---------------------------+-------------------------- %C A382688 2 | A020760 | A000007*10 %C A382688 3 | A010513/10 | A010716 %C A382688 4 | A372267, A372268 | A382103, A382104 %C A382688 5 | A372269, A372270 | A382105, A382106 %C A382688 6 | A372271, A372272, A372273 | A382107, A382686, A382687 %C A382688 7 | A372274, A372275, A372276 | this sequence, A382689, A382690 %H A382688 A.H.M. Smeets, <a href="/A382688/b382688.txt">Table of n, a(n) for n = 0..10000</a> %H A382688 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 25.4, n=7. %H A382688 A.H.M. Smeets, <a href="/A382103/a382103.py.txt">Python program for Legendre-Gauss quadrature constants.</a> %H A382688 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Legendre-GaussQuadrature.html">Legendre-Gauss Quadrature</a>. %e A382688 0.3818300505051189449503697754889751338783650835338627... %Y A382688 Cf. A372274. %K A382688 nonn,cons %O A382688 0,1 %A A382688 _A.H.M. Smeets_, Apr 03 2025