Definition:AlSalamChihara

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The LaTeX DLMF and DRMF macro \AlSalamChihara represents the Al-Salam Chihara polynomial.

This macro is in the category of polynomials.

In math mode, this macro can be called in the following ways:

\AlSalamChihara{n} produces ${\displaystyle{\displaystyle{\displaystyle Q_{n}}}}$

\AlSalamChihara{n}@{x}{a}{b}{q} produces ${\displaystyle{\displaystyle{\displaystyle Q_{n}\!\left(x;a,b\,|\,q\right)}}}$

\AlSalamChihara{n}@@{x}{a}{b}{q} produces ${\displaystyle{\displaystyle{\displaystyle Q_{n}\!\left(x\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle Q_{n}\!\left(x;a,b\,|\,q\right):=\frac{\left(ab;q\right)_{n}}{a^{n}}\,\qHyperrphis{3}{2}@@{q^{-n},a{\mathrm{e}^{i\theta}},a{\mathrm{e}^{-i\theta}}}{ab,0}{q}{q}}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle Q_{n}}}}$ : Al-Salam-Chihara polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamChihara
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11

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