Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit matrix inverses for lower triangular matrices with entries
  involving continuous q-ultraspherical polynomials   For a one-parameter family of lower triangular matrices with entries
involving continuous $q$-ultraspherical polynomials we give an explicit lower
triangular inverse matrix, with entries involving again continuous
$q$-ultraspherical functions. The matrices are $q$-analogues of results given
by Cagliero and Koornwinder recently. The proofs are not $q$-analogues of the
Cagliero-Koornwinder case, but are of a different nature involving $q$-Racah
polynomials. Some applications of these new formulas are given. Also the limit
$\beta \to 0$ is studied and gives rise to continuous $q$-Hermite polynomials
for $0 < q < 1$ and $q > 1$.

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The categories of this paper are: hep-ph
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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: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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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: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga