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A382690
Decimal expansion of the weight factor for Legendre-Gauss quadrature corresponding to abscissa A372276.
13
1, 2, 9, 4, 8, 4, 9, 6, 6, 1, 6, 8, 8, 6, 9, 6, 9, 3, 2, 7, 0, 6, 1, 1, 4, 3, 2, 6, 7, 9, 0, 8, 2, 0, 1, 8, 3, 2, 8, 5, 8, 7, 4, 0, 2, 2, 5, 9, 9, 4, 6, 6, 6, 3, 9, 7, 7, 2, 0, 8, 6, 3, 8, 7, 2, 4, 6, 5, 5, 2, 3, 4, 9, 7, 2, 0, 4, 2, 3, 0, 8, 7, 1, 5, 6, 2, 5
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
7 | A372274, A372275, A372276 | A382688, A382689, 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=7.
Eric Weisstein's World of Mathematics, Legendre-Gauss Quadrature.
EXAMPLE
0.12948496616886969327061143267908201832858740225994666...
CROSSREFS
Cf. A372276.
Sequence in context: A202324 A199267 A115290 * A273842 A371852 A021343
KEYWORD
nonn,cons
AUTHOR
A.H.M. Smeets, Apr 03 2025
STATUS
approved