Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform formulae for coefficients of meromorphic functions in two
  variables. Part I   Uniform asymptotic formulae for arrays of complex numbers of the form
$(f_{r,s})$, with $r$ and $s$ nonnegative integers, are provided as $r$ and $s$
converge to infinity at a comparable rate. Our analysis is restricted to the
case in which the generating function $F(z,w):=\sum f_{r,s} z^r w^s$ is
meromorphic in a neighborhood of the origin. We provide uniform asymptotic
formulae for the coefficients $f_{r,s}$ along directions in the $(r,s)$-lattice
determined by regular points of the singular variety of $F$. Our main result
derives from the analysis of a one dimensional parameter-varying integral
describing the asymptotic behavior of $f_{r,s}$. We specifically consider the
case in which the phase term of this integral has a unique stationary point,
however, allowing the possibility that one or more stationary points of the
amplitude term coalesce with this. Our results find direct application in
certain problems associated to the Lagrange inversion formula as well as
bivariate generating functions of the form $v(z)/(1-w\cdot u(z))$.

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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: nlin