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A382690 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372276.

%I A382690 #9 May 01 2025 21:41:59
%S A382690 1,2,9,4,8,4,9,6,6,1,6,8,8,6,9,6,9,3,2,7,0,6,1,1,4,3,2,6,7,9,0,8,2,0,
%T A382690 1,8,3,2,8,5,8,7,4,0,2,2,5,9,9,4,6,6,6,3,9,7,7,2,0,8,6,3,8,7,2,4,6,5,
%U A382690 5,2,3,4,9,7,2,0,4,2,3,0,8,7,1,5,6,2,5
%N A382690 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372276.
%C A382690 There are floor(k/2) positive zeros of the Legendre polynomial of degree k:
%C A382690  k | zeros                     | corresponding weights
%C A382690 ---+---------------------------+--------------------------
%C A382690  2 | A020760                   | A000007*10
%C A382690  3 | A010513/10                | A010716
%C A382690  4 | A372267, A372268          | A382103, A382104
%C A382690  5 | A372269, A372270          | A382105, A382106
%C A382690  6 | A372271, A372272, A372273 | A382107, A382686, A382687
%C A382690  7 | A372274, A372275, A372276 | A382688, A382689, this sequence
%H A382690 A.H.M. Smeets, <a href="/A382690/b382690.txt">Table of n, a(n) for n = 0..10000</a>
%H A382690 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 A382690 A.H.M. Smeets, <a href="/A382103/a382103.py.txt">Python program for Legendre-Gauss quadrature constants.</a>
%H A382690 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Legendre-GaussQuadrature.html">Legendre-Gauss Quadrature</a>.
%e A382690 0.12948496616886969327061143267908201832858740225994666...
%Y A382690 Cf. A372276.
%K A382690 nonn,cons
%O A382690 0,2
%A A382690 _A.H.M. Smeets_, Apr 03 2025