Definition:ctsqJacobi

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The LaTeX DLMF and DRMF macro \ctsqJacobi represents the continuous -Jacobi polynomial.

This macro is in the category of polynomials.

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

\ctsqJacobi{\alpha}{\beta}{m} produces Failed to parse (unknown function "\ctsqJacobi"): {\displaystyle {\displaystyle \ctsqJacobi{\alpha}{\beta}{m}}}
\ctsqJacobi{\alpha}{\beta}{m}@{x}{q} produces Failed to parse (unknown function "\ctsqJacobi"): {\displaystyle {\displaystyle \ctsqJacobi{\alpha}{\beta}{m}@{x}{q}}}

These are defined by
Failed to parse (unknown function "\ctsqJacobi"): {\displaystyle \ctsqJacobi{\alpha}{\beta}{n}@{x}{q} :=\frac{\qPochhammer{q^{\alpha+1}}{q}{n}}{\qPochhammer{q}{q}{n}} \qHyperrphis{4}{3}@@{q^{-n},q^{n+\alpha+\beta+1},q^{\frac{1}{2}\alpha+\frac{1}{4}}\expe^{i\theta},q^{\frac{1}{2}\alpha+\frac{1}{4}}\expe^{-i\theta}} {q^{\alpha+1},-q^{\frac{1}{2}(\alpha+\beta+1)},-q^{\frac{1}{2}(\alpha+\beta+2)}}{q}{q} }

with Failed to parse (syntax error): {\displaystyle x=\cos@@{\theta}} .

Symbols List

 : continuous -Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqJacobi
 : -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
 : cosine function : http://dlmf.nist.gov/4.14#E2