# Definition:AlSalamChihara

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 $\displaystyle \AlSalamChihara{n}$
\AlSalamChihara{n}@{x}{a}{b}{q} produces $\displaystyle \AlSalamChihara{n}@{x}{a}{b}{q}$
\AlSalamChihara{n}@@{x}{a}{b}{q} produces $\displaystyle \AlSalamChihara{n}@@{x}{a}{b}{q}$

These are defined by $\displaystyle \AlSalamChihara{n}@{x}{a}{b}{q}:=\frac{\qPochhammer{ab}{q}{n}}{a^n}\, \qHyperrphis{3}{2}@@{q^{-n},a\expe^{i\theta},a\expe^{-i\theta}}{ab,0}{q}{q}$

## Symbols List

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