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

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, 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, 8, 2, 6, 7, 1, 5, 2, 5, 1, 2, 4, 5, 6, 9, 7, 5, 5, 6, 2

Offset: 0

Author

A.H.M. Smeets, Mar 27 2025

Keywords

• nonn
• cons

Comments

There are floor(k/2) positive zeros of the Legendre polynomial of degree k:

k | zeros | corresponding weights

---+---------------------------+--------------------------

2 | A020760 | A000007*10

3 | A010513/10 | A010716

4 | A372267, A372268 | A382103, A382104

5 | A372269, A372270 | this sequence, A382106

6 | A372271, A372272, A372273 | A382107, A382686, A382687

7 | A372274, A372275, A372276 | A382688, A382689, A382690

Examples

			0.47862867049936646804129151483563819291229555334...
		

Links

• A.H.M. Smeets, Table of n, a(n) for n = 0..10000
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, (1972) Table 25.4, n=5.
• A.H.M. Smeets, Python program for Legendre-Gauss quadrature constants.
• Eric Weisstein's World of Mathematics, Legendre-Gauss Quadrature.

Crossrefs

Cf. A372269.

Formula

Equals (322+13*sqrt(70))/900.