Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dual addition formulas: the case of continuous $q$-ultraspherical and
  $q$-Hermite polynomials   We settle the dual addition formula for continuous $q$-ultraspherical
polynomials as an expansion in terms of special $q$-Racah polynomials for which
the constant term is given by the linearization formula for the continuous
$q$-ultraspherical polynomials. In a second proof we derive the dual addition
formula from the Rahman--Verma addition formula for these polynomials by using
the self-duality of the polynomials. We also consider the limit case of
continuous $q$-Hermite polynomials.

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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: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: econ