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A382103 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372267.

%I A382103 #29 Apr 12 2025 12:19:00
%S A382103 3,4,7,8,5,4,8,4,5,1,3,7,4,5,3,8,5,7,3,7,3,0,6,3,9,4,9,2,2,1,9,9,9,4,
%T A382103 0,7,2,3,5,3,4,8,6,9,5,8,3,3,8,9,3,5,4,0,4,9,2,5,2,9,3,1,9,5,1,8,7,5,
%U A382103 1,8,6,7,4,6,5,9,1,0,3,5,1,7,2,1,9,8,3
%N A382103 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372267.
%C A382103 There are floor(k/2) positive zeros of the Legendre polynomial of degree k:
%C A382103    k | zeros                     | corresponding weights for Legendre-Gauss quadrature
%C A382103   ---+---------------------------+----------------------------------------------------
%C A382103    2 | A020760                   | A000007*10
%C A382103    3 | A010513/10                | A010716
%C A382103    4 | A372267, A372268          | this sequence, A382104
%C A382103    5 | A372269, A372270          | A382105, A382106
%C A382103    6 | A372271, A372272, A372273 | A382107, A382686, A382687
%C A382103    7 | A372274, A372275, A372276 | A382688, A382689, A382690
%H A382103 A.H.M. Smeets, <a href="/A382103/b382103.txt">Table of n, a(n) for n = 0..10000</a>
%H A382103 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 A382103 A.H.M. Smeets, <a href="/A382103/a382103.py.txt">Python program for Legendre-Gauss quadrature constants</a>.
%H A382103 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Legendre-GaussQuadrature.html">Legendre-Gauss Quadrature</a>.
%F A382103 Equals 1/2 - (1/6)*sqrt(5/6).
%e A382103 0.34785484513745385737306394922199940723534869583389...
%t A382103 RealDigits[1/2 - Sqrt[5/6]/6, 10, 120][[1]] (* _Amiram Eldar_, Mar 24 2025 *)
%Y A382103 Cf. A372267.
%K A382103 nonn,cons
%O A382103 0,1
%A A382103 _A.H.M. Smeets_, Mar 15 2025