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Search: id:A120080
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| A120080 |
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Numerators of expansion of original Debye function D(3,x). |
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+0
2
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| 1, -3, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -691, 0, 1, 0, -3617, 0, 43867, 0, -174611, 0, 77683, 0, -236364091, 0, 657931, 0, -3392780147, 0, 1723168255201, 0, -7709321041217, 0, 151628697551, 0, -26315271553053477373
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OFFSET
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0,2
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COMMENT
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Denominators are given in A120081.
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REFERENCES
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L. D. Landau, E. M. Lifschitz: Lehrbuch der Theoretischen Physik, Band V: Statistische Physik, Akademie Verlag, Leipzig, p. 197, equ. (63.5).
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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].
W. Lang: Rationals r(n).
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, December 1972, pp. 998, equ. 27.1.1 for n=3, with a factor (x^3)/3 extracted.
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FORMULA
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D(x)=D(3,x):= (3/x^3)*int(t^3/(exp(t)-1),t,0,x).
a(n)=numerator(r(n)), with r(n):=[x^n](1-3*x/8+sum((B(2*k)/((2*k+3)*(2*k)!))*x^(2*k), 0,..infinity)) (in lowest terms), |x|<2*pi. B(2*k):=A000367(k)/A002445(k) (Bernoulli numbers).
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EXAMPLE
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Rationals r(n): [1,-3/8,1/20,0,1/1680,0,1/90720,0,...].
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CROSSREFS
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Sequence in context: A034370 A127537 A025443 this_sequence A111700 A060096 A051834
Adjacent sequences: A120077 A120078 A120079 this_sequence A120081 A120082 A120083
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KEYWORD
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sign,frac
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 20 2006
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