Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On peculiar properties of generating functions of some orthogonal
  polynomials   We prove that for |x|,|t|<1, -1 <q \leq1 and n\geq0:
\Sigma_{i\geq0}((t^{i})/((q)_{i}))h_{n+i}(x|q) = h_{n}(x|t,q)
\Sigma_{i\geq0}((t^{i})/((q)_{i}))h_{i}(x|q), where h_{n}(x|q) and h_{n}(x|t,q)
are respectively the so called q-Hermite and the big q-Hermite polynomials and
(q)_{n} denotes the so called q-Pochhammer symbol. We prove similar equalities
involving big q-Hermite and Al-Salam---Chihara (ASC) polynomials and ASC and
the so called continuous dual q-Hahn (c2h) polynomials. Moreover we are able to
relate in this way some other 'ordinary ' orthogonal polynomials such as e.g.
Hermite, Chebyshev or Laguerre. These equalities give new interpretation of the
polynomials involved and moreover can give rise to a simple method of
generating more and more general (i.e. involving more and more parameters)
families of orthogonal polynomials. We pose some conjectures concerning
Askey--Wilson polynomials and their possible generalizations. We prove that
these conjectures are true for the cases q = 1 (classical case) and q = 0 (free
case) thus paving the way to generalization of AW polynomials at least in these
two cases.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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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: nlin
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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: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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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: supr-con