A382106 - OEIS

A382106

Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372270.

2, 3, 6, 9, 2, 6, 8, 8, 5, 0, 5, 6, 1, 8, 9, 0, 8, 7, 5, 1, 4, 2, 6, 4, 0, 4, 0, 7, 1, 9, 9, 1, 7, 3, 6, 2, 6, 4, 3, 2, 6, 0, 0, 0, 2, 2, 1, 2, 4, 1, 4, 0, 1, 5, 5, 8, 2, 8, 2, 7, 8, 8, 8, 2, 2, 1, 7, 1, 7, 2, 8, 8, 4, 0, 3, 0, 4, 3, 0, 9, 8, 5, 7, 9, 9, 9, 3

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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 | A382106, this sequence

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

7 | A372274, A372275, A372276 | A382688, A382689, 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=5.

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

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

Index entries for algebraic numbers, degree 2.

FORMULA

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

EXAMPLE

0.236926885056189087514264040719917362643260002212...

MATHEMATICA

First[RealDigits[(322 - 13*Sqrt[70])/9, 10, 100]] (* Paolo Xausa, Nov 25 2025 *)

CROSSREFS

Cf. A372270.

Sequence in context: A088329 A193079 A191397 * A358764 A361133 A361534