Geodesic
A new method for computing asymptotics of diagonal coefficients of multivariate generating functions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) (2007).

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Let $\sum_{\mathbf{n} \in \mathbb{N}^d} F_{\mathbf{n}} \mathbf{x}^{\mathbf{n}}$ 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. Several examples are given in detail. 
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     author = {Raichev, Alexander and Wilson, Mark C.},
     title = {A new method for computing asymptotics of diagonal coefficients of multivariate generating functions},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07)},
     year = {2007},
     doi = {10.46298/dmtcs.3531},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3531/}
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Raichev, Alexander; Wilson, Mark C. A new method for computing asymptotics of diagonal coefficients of multivariate generating functions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) (2007). doi : 10.46298/dmtcs.3531. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3531/

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