Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hypergeometric expression for the resolvent of the discrete Laplacian in
  low dimensions   We present an explicit formula for the resolvent of the discrete Laplacian on
the square lattice, and compute its asymptotic expansions around thresholds in
low dimensions. As a by-product we obtain a closed formula for the fundamental
solution to the discrete Laplacian. For the proofs we express the resolvent in
a general dimension in terms of the Appell--Lauricella hypergeometric function
of type $C$ outside a disk encircling the spectrum. In low dimensions it
reduces to a generalized hypergeometric function, for which certain
transformation formulas are available for the desired expansions.

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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio