Displaying similar documents to “Asymptotics of coefficients of multivariate generating functions: Improvements for smooth points.”

A variant of the complex Liouville-Green approximation theorem

Renato Spigler, Marco Vianello (2000)

Archivum Mathematicum

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We propose a variant of the classical Liouville-Green approximation theorem for linear complex differential equations of the second order. We obtain rigorous error bounds for the asymptotics at infinity, in the spirit of F. W. J. Olver’s formulation, by using rather arbitrary ξ -progressive paths. This approach can provide higher flexibility in practical applications of the method.

Ascents of size less than d in compositions

Maisoon Falah, Toufik Mansour (2011)

Open Mathematics

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A composition of a positive integer n is a finite sequence π1π2...πm of positive integers such that π1+...+πm = n. Let d be a fixed number. We say that we have an ascent of size d or more (respectively, less than d) if πi+1 ≥ πi+d (respectively, πi < πi+1 < πi + d). Recently, Brennan and Knopfmacher determined the mean, variance and limiting distribution of the number of ascents of size d or more in the set of compositions of n. In this paper, we find an explicit formula for the...