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A382104 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372268.

%I A382104 #27 May 23 2025 01:14:16
%S A382104 6,5,2,1,4,5,1,5,4,8,6,2,5,4,6,1,4,2,6,2,6,9,3,6,0,5,0,7,7,8,0,0,0,5,
%T A382104 9,2,7,6,4,6,5,1,3,0,4,1,6,6,1,0,6,4,5,9,5,0,7,4,7,0,6,8,0,4,8,1,2,4,
%U A382104 8,1,3,2,5,3,4,0,8,9,6,4,8,2,7,8,0,1,6
%N A382104 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372268.
%C A382104 There are floor(k/2) positive zeros of the Legendre polynomial of degree k:
%C A382104    k | zeros                     | corresponding weights for Legendre-Gauss quadrature
%C A382104   ---+---------------------------+----------------------------------------------------
%C A382104    2 | A020760                   | A000007*10
%C A382104    3 | A010513/10                | A010716
%C A382104    4 | A372267, A372268          | A382103, this sequence
%C A382104    5 | A372269, A372270          | A382105, A382106
%C A382104    6 | A372271, A372272, A372273 | A382107, A382686, A382687
%C A382104    7 | A372274, A372275, A372276 | A382688, A382689, A382690
%H A382104 A.H.M. Smeets, <a href="/A382104/b382104.txt">Table of n, a(n) for n = 0..10000</a>
%H A382104 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=4.
%H A382104 A.H.M. Smeets, <a href="/A382103/a382103.py.txt">Python program for Legendre-Gauss quadrature constants</a>.
%H A382104 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Legendre-GaussQuadrature.html">Legendre-Gauss Quadrature</a>.
%F A382104 Equals 1/2 + (1/6)*sqrt(5/6).
%F A382104 Minimal polynomial: 216*x^2 - 216*x + 49. - _Stefano Spezia_, May 22 2025
%e A382104 0.65214515486254614262693605077800059276465130416610645...
%t A382104 RealDigits[1/2 + Sqrt[5/6]/6, 10, 120][[1]] (* _Amiram Eldar_, Mar 24 2025 *)
%o A382104 (PARI) 1/2 + (1/6)*sqrt(5/6) \\ _Stefano Spezia_, May 22 2025
%Y A382104 Cf. A372268.
%K A382104 nonn,cons
%O A382104 0,1
%A A382104 _A.H.M. Smeets_, Mar 15 2025