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A382687
Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372273.
13
1, 7, 1, 3, 2, 4, 4, 9, 2, 3, 7, 9, 1, 7, 0, 3, 4, 5, 0, 4, 0, 2, 9, 6, 1, 4, 2, 1, 7, 2, 7, 3, 2, 8, 9, 3, 5, 2, 6, 8, 2, 2, 5, 0, 1, 4, 8, 4, 0, 4, 3, 9, 8, 2, 3, 9, 8, 6, 3, 5, 4, 3, 9, 7, 9, 8, 9, 4, 5, 7, 6, 0, 5, 4, 2, 3, 4, 0, 1, 5, 4, 6, 4, 7, 9, 2, 7
OFFSET
0,2
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
6 | A372271, A372272, A372273 | A382107, A382686, this sequence
LINKS
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.
Eric Weisstein's World of Mathematics, Legendre-Gauss Quadrature.
EXAMPLE
0.17132449237917034504029614217273289352682250148404...
PROG
(PARI) polrootsreal(2025000*x^3 - 2025000*x^2 + 629325*x - 58564)[1] \\ conjectured; Charles R Greathouse IV, Nov 17 2025
CROSSREFS
Cf. A372273.
Sequence in context: A342377 A346103 A039616 * A344967 A362923 A201585
KEYWORD
nonn,cons
AUTHOR
A.H.M. Smeets, Apr 03 2025
STATUS
approved