Asymptotic behaviour of continued fraction coefficients related to singularities of the weight function
(1985) Recursion Method and Its Applications. Proceedings of a Conference — Location: London, UK (13.September.1984)
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- Abstract
- In the continued fraction expansion G/sub 0/(z)= int /sub sigma /(z-E)/sup -1/n/sub 0 /(E)dE=1/(z-a/sub 0/-b/sub 1//sup 2//(z-a/sub 1 /-. . .)), one examines relations between features of the local density of states (weight function) n/sub 0/, positive on sigma , and the coefficients {a/sub n/,b/sub n/}. The asymptotic description of a/sub n/ and b/sub n/ is based on two elements: the main asymptotic behaviour depends on the band structure of sigma :{a/sub n/} and {b/sub n/} converge towards limits in the single band case, oscillate endlessly in a predictable way in the multiband case (Ducastelle); damped oscillations are created by isolated singularities of n/sub 0/. The period of the oscillations is related to the position of the singularity, the rate of damping is related to the nature of the singularity. The present study contains a description of the effects of Van Hove, algebraic (or Jacobi), and Lifshitz singularities.
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Magnus, A. (1985). Asymptotic behaviour of continued fraction coefficients related to singularities of the weight function. In Pettifor, D.G.; Weaire, D.L.; (ed.), Recursion Method and Its Applications. Proceedings of a Conference (p. p. 22-45). Springer-verlag. https://hdl.handle.net/2078.5/229876