Definition:AlSalamIsmail
The LaTeX DLMF and DRMF macro \AlSalamIsmail represents the Al-Salam Ismail Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \AlSalamIsmail{n}}}
- \AlSalamIsmail{n}@{x}{s}{q} produces Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \AlSalamIsmail{n}@{x}{s}{q}}}
These are defined by
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle U_{n}}}
: Al-Salam Ismail polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamIsmail
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle {{}_{r}\phi_{s}}}}
: basic hypergeometric (or Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}}
-hypergeometric) function : http://dlmf.nist.gov/17.4#E1