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 Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \AlSalamChiharain 1:31"): {\displaystyle {\displaystyle \AlSalamChihara{n}}}
\AlSalamChihara{n}@{x}{a}{b}{q} produces Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \AlSalamChiharain 1:31"): {\displaystyle {\displaystyle \AlSalamChihara{n}@{x}{a}{b}{q}}}
\AlSalamChihara{n}@@{x}{a}{b}{q} produces Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \AlSalamChiharain 1:31"): {\displaystyle {\displaystyle \AlSalamChihara{n}@@{x}{a}{b}{q}}}

These are defined by Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \AlSalamChiharain 2:1"): {\displaystyle {\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

 : Al-Salam-Chihara polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamChihara
 : -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
 : basic hypergeometric (or -hypergeometric) function : http://dlmf.nist.gov/17.4#E1
 : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11