cp's OEIS Frontend

A382689 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372275.

%I A382689 #8 Apr 24 2025 16:41:24
%S A382689 2,7,9,7,0,5,3,9,1,4,8,9,2,7,6,6,6,7,9,0,1,4,6,7,7,7,1,4,2,3,7,7,9,5,
%T A382689 8,2,4,8,6,9,2,5,0,6,5,2,2,6,5,9,8,7,6,4,5,3,7,0,1,4,0,3,2,6,9,3,6,1,
%U A382689 8,8,1,0,4,3,0,5,6,2,6,7,6,8,1,3,2,4,0
%N A382689 Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372275.
%C A382689 There are floor(k/2) positive zeros of the Legendre polynomial of degree k:
%C A382689  k | zeros                     | corresponding weights
%C A382689 ---+---------------------------+--------------------------
%C A382689  2 | A020760                   | A000007*10
%C A382689  3 | A010513/10                | A010716
%C A382689  4 | A372267, A372268          | A382103, A382104
%C A382689  5 | A372269, A372270          | A382105, A382106
%C A382689  6 | A372271, A372272, A372273 | A382107, A382686, A382687
%C A382689  7 | A372274, A372275, A372276 | A382688, this sequence, A382690
%H A382689 A.H.M. Smeets, <a href="/A382689/b382689.txt">Table of n, a(n) for n = 0..10000</a>
%H A382689 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 A382689 A.H.M. Smeets, <a href="/A382103/a382103.py.txt">Python program for Legendre-Gauss quadrature constants.</a>
%H A382689 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Legendre-GaussQuadrature.html">Legendre-Gauss Quadrature</a>.
%e A382689 0.279705391489276667901467771423779582486925065226598764...
%Y A382689 Cf. A372275.
%K A382689 nonn,cons
%O A382689 0,1
%A A382689 _A.H.M. Smeets_, Apr 03 2025