Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-symmetric Jacobi and Wilson type polynomials   Consider a root system of type $BC_1$ on the real line $\mathbb R$ with
general positive multiplicities. The Cherednik-Opdam transform defines a
unitary operator from an $L^2$-space on $\mathbb R$ to a $L^2$-space of
$\mathbb C^2$-valued functions on $\mathbb R^+$ with the Harish-Chandra measure
$|c(\lam)|^{-2}d\lam$.
  By introducing a weight function of the form $\cosh^{-\sig}(t)\tanh^{2k} t$
on $\mathbb R$ we find an orthogonal basis for the $L^2$-space on $\mathbb R$
consisting of even and odd functions expressed in terms of the Jacobi
polynomials (for each fixed $\sig$ and $k$). We find a Rodrigues type formula
for the functions in terms of the Cherednik operator. We compute explicitly
their Cherednik-Opdam transforms. We discover thus a new family of $\mathbb
C^2$-valued orthogonal polynomials. In the special case when $k=0$ the even
polynomials become Wilson polynomials, and the corresponding result was proved
earlier by Koornwinder.

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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg