Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact, explicit and entire solutions to a nontrivial finite-difference
  equation and their applications   Below, the explicit solution to a certain finite-difference equation is given
and the required steps for derivation of these results are outlined. Everything
is included as Mathematica formulae, so the notebook itself can be used for
checking and improving the present results. Some important references for
justifying some steps and crosschecking certain results have been included.
Full references and derivations will be made available shortly. It should be
noted that several applications for the solutions have been included at the end
of the document. These include at least diagonalisation of certain infinite
matrices, definition of isospectral operators with simple eigenvalues and
alternative representation of a solution to a problem related to black holes.
Additionally, the corresponding, discretised associated Laguerre polynomials
are defined explicitly.

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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex