A new method for computing asymptotics of diagonal coefficients of multivariate generating functions

Alexander Raichev and Mark C. Wilson, to appear in Proceedings of the International Conference on Analysis of Algorithms (Juan-les-Pins, June 2007).

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Let sum_{mathbf{n}inmathbb{N}^d} f_{mathbf{n}} mathbf{x}^mathbf{n} be a multivariate generating function that converges in a neighborhood of the origin of mathbb{C}^d. We present a new, multivariate method for computing the asymptotics of the diagonal coefficients f_{a_1n,ldots,a_dn} and show its superiority over the standard, univariate diagonal method.

Note: there is a typo: in Example 3.6, we should have c = ( (L-b)/a, (L-a)/b ) where L = sqrt{a^2 + b^2}.

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