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Search: id:A130757
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| A130757 |
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Triangular table of coefficients of Laguerre-Sonin polynomials n!*2^(n-m)*L(n,1/2,x). |
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+0
6
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| 1, 3, -1, 15, -10, 1, 105, -105, 21, -1, 945, -1260, 378, -36, 1, 10395, -17325, 6930, -990, 55, -1, 135135, -270270, 135135, -25740, 2145, -78, 1, 2027025, -4729725, 2837835, -675675, 75075, -4095, 105, -1, 34459425, -91891800, 64324260, -18378360, 2552550, -185640, 7140, -136
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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These polynomials appear in the radial l=0 (s) wave functions of the isotropic three dimensional harmonic quantum oscillator with the dimensionless variable x=(r/L)^2 with r>=0 and L^2=h/(m*f0). h is Planck's constant and m and f0 are the mass and the frequency of the oscillator.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, December 1972, p. 775, 22.3.9.
W. Lang, First ten rows and more.
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FORMULA
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a(n,m)= n!*(2^(n-m))*L(1/2,n,m) with L(1/2,n,m)=((-1)^m)*binomial(n+1/2,n-m)/m!, n>=m>=0, else 0.
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EXAMPLE
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[1]; [3,-1]; [15,-10,1]; [105,-105,21,-1]; [945,-1260,378,-36,1]; ...
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CROSSREFS
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Cf. A021009 (Coefficient table of n!*L(n, 0, x).
Row sums (signed) give A131441. Row sums (unsigned) give A066224.
Sequence in context: A035342 A039815 A134685 this_sequence A014621 A113378 A095922
Adjacent sequences: A130754 A130755 A130756 this_sequence A130758 A130759 A130760
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KEYWORD
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sign,tabl,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 13 2007
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