Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial identities associated with a bivariate generating function
  for overpartition pairs   We obtain a three-parameter $q$-series identity that generalizes two results
of Chan and Mao. By specializing our identity, we derive new results of
combinatorial significance in connection with $N(r, s, m, n)$, a function
counting certain overpartition pairs recently introduced by Bringmann, Lovejoy
and Osburn. For example, one of our identities gives a closed-form evaluation
of a double series in terms of Chebyshev polynomials of the second kind,
thereby resulting in an analogue of Euler's pentagonal number theorem. Another
of our results expresses a multi-sum involving $N(r, s, m, n)$ in terms of just
the partition function $p(n)$. Using a result of Shimura we also relate a
certain double series with a weight 7/2 theta series.

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The categories of this paper are: gr-qc
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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: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int