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A382106 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372270.

%I A382106 #13 Apr 12 2025 09:50:17
%S A382106 2,3,6,9,2,6,8,8,5,0,5,6,1,8,9,0,8,7,5,1,4,2,6,4,0,4,0,7,1,9,9,1,7,3,
%T A382106 6,2,6,4,3,2,6,0,0,0,2,2,1,2,4,1,4,0,1,5,5,8,2,8,2,7,8,8,8,2,2,1,7,1,
%U A382106 7,2,8,8,4,0,3,0,4,3,0,9,8,5,7,9,9,9,3
%N A382106 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372270.
%C A382106 There are floor(k/2) positive zeros of the Legendre polynomial of degree k:
%C A382106  k | zeros                     | corresponding weights
%C A382106 ---+---------------------------+--------------------------
%C A382106  2 | A020760                   | A000007*10
%C A382106  3 | A010513/10                | A010716
%C A382106  4 | A372267, A372268          | A382103, A382104
%C A382106  5 | A372269, A372270          | A382106, this sequence
%C A382106  6 | A372271, A372272, A372273 | A382107, A382686, A382687
%C A382106  7 | A372274, A372275, A372276 | A382688, A382689, A382690
%H A382106 A.H.M. Smeets, <a href="/A382106/b382106.txt">Table of n, a(n) for n = 0..10000</a>
%H A382106 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=5.
%H A382106 A.H.M. Smeets, <a href="/A382103/a382103.py.txt">Python program for Legendre-Gauss quadrature constants.</a>
%H A382106 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Legendre-GaussQuadrature.html">Legendre-Gauss Quadrature</a>.
%F A382106 Equals (322-13*sqrt(70))/900.
%e A382106 0.236926885056189087514264040719917362643260002212...
%Y A382106 Cf. A372270.
%K A382106 nonn,cons
%O A382106 0,1
%A A382106 _A.H.M. Smeets_, Mar 27 2025