Convolutions of inverse linear functions via multivariate residues

Let F (z1, . . . zd) = ∏n j=1 η lj(z1,...,zd) nj be the quotient of an analytic function by a product of linear functions lj := 1− ∑ bijzi. We compute asymptotic formulae for the Taylor coefficients of F via the multivariate residue approach begun by [BM93]. By means of stratified Morse theory, we are able to give a short and fully implementable algorithm for determining an asymptotic series expansion.

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