Definition:qinvAlSalamChihara

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The LaTeX DLMF and DRMF macro \qinvAlSalamChihara represents the ${\displaystyle{\displaystyle q}}$-inverse of 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:

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

\qinvAlSalamChihara{n}@{x}{a}{b}{q^{-1}} produces ${\displaystyle{\displaystyle{\displaystyle Q_{n}\!\left(x;a,b\,;\,q^{-1}\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle Q_{n}\!\left(\thalf(aq^{-x}+a^{-1}q^{x});a,b\,;\,q^{-1}\right):=(-1)^{n}b^{n}q^{-\frac{1}{2}n(n-1)}\left((ab)^{-1};q\right)_{n}\qHyperrphis{3}{1}@@{q^{-n},q^{-x},a^{-2}q^{x}}{(ab)^{-1}}{q}{q^{n}ab^{-1}}}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle Q_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-inverse Al-Salam-Chihara polynomial : http://dlmf.nist.gov/23.1
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-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

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