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 A382687 #9 Apr 24 2025 16:40:59 %S A382687 1,7,1,3,2,4,4,9,2,3,7,9,1,7,0,3,4,5,0,4,0,2,9,6,1,4,2,1,7,2,7,3,2,8, %T A382687 9,3,5,2,6,8,2,2,5,0,1,4,8,4,0,4,3,9,8,2,3,9,8,6,3,5,4,3,9,7,9,8,9,4, %U A382687 5,7,6,0,5,4,2,3,4,0,1,5,4,6,4,7,9,2,7 %N A382687 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372273. %C A382687 There are floor(k/2) positive zeros of the Legendre polynomial of degree k: %C A382687 k | zeros | corresponding weights %C A382687 ---+---------------------------+-------------------------- %C A382687 2 | A020760 | A000007*10 %C A382687 3 | A010513/10 | A010716 %C A382687 4 | A372267, A372268 | A382103, A382104 %C A382687 5 | A372269, A372270 | A382105, A382106 %C A382687 6 | A372271, A372272, A372273 | A382107, A382686, this sequence %C A382687 7 | A372274, A372275, A372276 | A382688, A382689, A382690 %H A382687 A.H.M. Smeets, <a href="/A382687/b382687.txt">Table of n, a(n) for n = 0..10000</a> %H A382687 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=6. %H A382687 A.H.M. Smeets, <a href="/A382103/a382103.py.txt">Python program for Legendre-Gauss quadrature constants.</a> %H A382687 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Legendre-GaussQuadrature.html">Legendre-Gauss Quadrature</a>. %e A382687 0.17132449237917034504029614217273289352682250148404... %Y A382687 Cf. A372273. %K A382687 nonn,cons %O A382687 0,2 %A A382687 _A.H.M. Smeets_, Apr 03 2025