cp's OEIS Frontend

A382105 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372269.

%I A382105 #18 Apr 12 2025 09:50:13
%S A382105 4,7,8,6,2,8,6,7,0,4,9,9,3,6,6,4,6,8,0,4,1,2,9,1,5,1,4,8,3,5,6,3,8,1,
%T A382105 9,2,9,1,2,2,9,5,5,5,3,3,4,3,1,4,1,5,3,9,9,7,2,7,2,7,6,6,7,3,3,3,8,3,
%U A382105 8,2,6,7,1,5,2,5,1,2,4,5,6,9,7,5,5,6,2
%N A382105 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372269.
%C A382105 There are floor(k/2) positive zeros of the Legendre polynomial of degree k:
%C A382105  k | zeros                     | corresponding weights
%C A382105 ---+---------------------------+--------------------------
%C A382105  2 | A020760                   | A000007*10
%C A382105  3 | A010513/10                | A010716
%C A382105  4 | A372267, A372268          | A382103, A382104
%C A382105  5 | A372269, A372270          | this sequence, A382106
%C A382105  6 | A372271, A372272, A372273 | A382107, A382686, A382687
%C A382105  7 | A372274, A372275, A372276 | A382688, A382689, A382690
%H A382105 A.H.M. Smeets, <a href="/A382105/b382105.txt">Table of n, a(n) for n = 0..10000</a>
%H A382105 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) Table 25.4, n=5.
%H A382105 A.H.M. Smeets, <a href="/A382103/a382103.py.txt">Python program for Legendre-Gauss quadrature constants.</a>
%H A382105 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Legendre-GaussQuadrature.html">Legendre-Gauss Quadrature</a>.
%F A382105 Equals (322+13*sqrt(70))/900.
%e A382105 0.47862867049936646804129151483563819291229555334...
%Y A382105 Cf. A372269.
%K A382105 nonn,cons
%O A382105 0,1
%A A382105 _A.H.M. Smeets_, Mar 27 2025