A382689 - OEIS

A382689

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

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, 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, 8, 8, 1, 0, 4, 3, 0, 5, 6, 2, 6, 7, 6, 8, 1, 3, 2, 4, 0

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

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 | A382105, A382106

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

7 | A372274, A372275, A372276 | A382688, this sequence, A382690

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 [alternative scanned copy]. Table 25.4, n=7.

A.H.M. Smeets, Python program for Legendre-Gauss quadrature constants.

Eric Weisstein's World of Mathematics, Legendre-Gauss Quadrature.

EXAMPLE

0.279705391489276667901467771423779582486925065226598764...

CROSSREFS

Cf. A372275.

Sequence in context: A011054 A276140 A130818 * A339237 A363078 A377479

Adjacent sequences: A382686 A382687 A382688 * A382690 A382691 A382692

KEYWORD

nonn,cons

AUTHOR

A.H.M. Smeets, Apr 03 2025

STATUS

approved