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 A382107 #11 Apr 24 2025 17:43:28 %S A382107 4,6,7,9,1,3,9,3,4,5,7,2,6,9,1,0,4,7,3,8,9,8,7,0,3,4,3,9,8,9,5,5,0,9, %T A382107 9,4,8,1,1,6,5,5,6,0,5,7,6,9,2,1,0,5,3,5,3,1,1,6,2,5,3,1,9,9,6,3,9,1, %U A382107 4,2,0,1,6,2,0,3,9,8,1,2,7,0,3,1,1,1,0 %N A382107 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372271. %C A382107 There are floor(k/2) positive zeros of the Legendre polynomial of degree k: %C A382107 k | zeros | corresponding weights %C A382107 ---+---------------------------+-------------------------- %C A382107 2 | A020760 | A000007*10 %C A382107 3 | A010513/10 | A010716 %C A382107 4 | A372267, A372268 | A382103, A382104 %C A382107 5 | A372269, A372270 | A382105, A382106 %C A382107 6 | A372271, A372272, A372273 | this sequence, A382686, A382687 %C A382107 7 | A372274, A372275, A372276 | A382688, A382689, A382690 %H A382107 A.H.M. Smeets, <a href="/A382107/b382107.txt">Table of n, a(n) for n = 0..10000</a> %H A382107 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 A382107 A.H.M. Smeets, <a href="/A382103/a382103.py.txt">Python program for Legendre-Gauss quadrature constants.</a> %H A382107 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Legendre-GaussQuadrature.html">Legendre-Gauss Quadrature</a>. %e A382107 0.4679139345726910473898703439895509948116556057692... %Y A382107 Cf. A372271. %K A382107 nonn,cons %O A382107 0,1 %A A382107 _A.H.M. Smeets_, Mar 27 2025