A382107 - OEIS

A382107

Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372271.

4, 6, 7, 9, 1, 3, 9, 3, 4, 5, 7, 2, 6, 9, 1, 0, 4, 7, 3, 8, 9, 8, 7, 0, 3, 4, 3, 9, 8, 9, 5, 5, 0, 9, 9, 4, 8, 1, 1, 6, 5, 5, 6, 0, 5, 7, 6, 9, 2, 1, 0, 5, 3, 5, 3, 1, 1, 6, 2, 5, 3, 1, 9, 9, 6, 3, 9, 1, 4, 2, 0, 1, 6, 2, 0, 3, 9, 8, 1, 2, 7, 0, 3, 1, 1, 1, 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 | this sequence, 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=6.

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

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

EXAMPLE

0.4679139345726910473898703439895509948116556057692...

MATHEMATICA

RealDigits[With[{x = Root[LegendreP[6, #] &, 4]}, 2*(1-x^2)/(49*LegendreP[7, x]^2)], 10, 120][[1]] (* Amiram Eldar, Apr 14 2026 *)

CROSSREFS

Cf. A372271.

Sequence in context: A078744 A024555 A363375 * A269330 A395470 A213627

Adjacent sequences: A382104 A382105 A382106 * A382108 A382109 A382110

KEYWORD

nonn,cons

AUTHOR

A.H.M. Smeets, Mar 27 2025

STATUS

approved