Definition:ctsqJacobi
The LaTeX DLMF and DRMF macro \ctsqJacobi represents the continuous Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q} -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 (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \ctsqJacobi{\alpha}{\beta}{m}}}
- \ctsqJacobi{\alpha}{\beta}{m}@{x}{q} produces Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \ctsqJacobi{\alpha}{\beta}{m}@{x}{q}}}
These are defined by
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x=\cos@@{\theta}}
.
Symbols List
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle P^{(\alpha,\beta)}_{n}}}
: continuous Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}}
-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqJacobi
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (a;q)_n}}
: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}}
-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
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
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{e}}}
: the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{cos}}}
: cosine function : http://dlmf.nist.gov/4.14#E2