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A382686 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372272.

%I A382686 #10 Apr 24 2025 16:41:12
%S A382686 3,6,0,7,6,1,5,7,3,0,4,8,1,3,8,6,0,7,5,6,9,8,3,3,5,1,3,8,3,7,7,1,6,1,
%T A382686 1,1,6,6,1,5,2,1,8,9,2,7,4,6,7,4,5,4,8,2,2,8,9,7,3,9,2,4,0,2,3,7,1,4,
%U A382686 0,0,3,7,8,3,7,2,6,1,7,1,8,3,2,0,9,6,2
%N A382686 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372272.
%C A382686 There are floor(k/2) positive zeros of the Legendre polynomial of degree k:
%C A382686  k | zeros                     | corresponding weights
%C A382686 ---+---------------------------+--------------------------
%C A382686  2 | A020760                   | A000007*10
%C A382686  3 | A010513/10                | A010716
%C A382686  4 | A372267, A372268          | A382103, A382104
%C A382686  5 | A372269, A372270          | A382105, A382106
%C A382686  6 | A372271, A372272, A372273 | A382107, this sequence, A382687
%C A382686  7 | A372274, A372275, A372276 | A382688, A382689, A382690
%H A382686 A.H.M. Smeets, <a href="/A382686/b382686.txt">Table of n, a(n) for n = 0..10000</a>
%H A382686 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 A382686 A.H.M. Smeets, <a href="/A382103/a382103.py.txt">Python program for Legendre-Gauss quadrature constants.</a>
%H A382686 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Legendre-GaussQuadrature.html">Legendre-Gauss Quadrature</a>.
%e A382686 0.36076157304813860756983351383771611166152189274674...
%Y A382686 Cf. A372272.
%K A382686 nonn,cons
%O A382686 0,1
%A A382686 _A.H.M. Smeets_, Apr 03 2025