# Definition:AlSalamIsmail

The LaTeX DLMF and DRMF macro **\AlSalamIsmail** represents the Al-Salam Ismail **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle q}**
polynomial.

This macro is in the category of polynomials.

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

**\AlSalamIsmail{n}**produces**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle \AlSalamIsmail{n}}}****\AlSalamIsmail{n}@{x}{s}{q}**produces**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle \AlSalamIsmail{n}@{x}{s}{q}}}**

These are defined by
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle \AlSalamIsmail{2n}@{x^{1/2}}{a}{b}:=q^{n^2-n}(-b)^n \qHyperrphis{4}{3}@@{q^{-n},-q^{1-n}/a,-aq^n,q^{n+1}} {-q,q^{1/2},-q^{1/2}} {q}{\frac{xaq}{b}} }**

and

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle \AlSalamIsmail{2n+1}@{x^{1/2}}{a}{b}=q^{n^2-n}\frac{(-b)^n(1+aq^n)(1-q^{n+1})x^{1/2}}{(1-q)} \qHyperrphis{4}{3}@@{q^{-n},-q^{1-n}/a,-aq^{n+1},q^{n+2}} {-q,q^{3/2},-q^{3/2}} {q}{\frac{xaq}{b}}. }**

## Symbols List

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle U_{n}}}**
: Al-Salam Ismail polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamIsmail

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle {{}_{r}\phi_{s}}}}**
: basic hypergeometric (or **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle q}}**
-hypergeometric) function : http://dlmf.nist.gov/17.4#E1