Definition:CiglerqChebyT

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Definition:CiglerqChebyU >>

The LaTeX DLMF and DRMF macro \CiglerqChebyT represents the Cigler ${\displaystyle{\displaystyle q}}$-Chebyshev polynomial of the first kind.

This macro is in the category of polynomials.

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

\CiglerqChebyT{n} produces ${\displaystyle{\displaystyle{\displaystyle T_{n}}}}$

\CiglerqChebyT{n}@{x}{s}{q} produces ${\displaystyle{\displaystyle{\displaystyle T_{n}\!\left(x,s,q\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle T_{n}\!\left(x,s,q\right):=(-s)^{\frac{1}{2}n}P_{n}\!\left((-qs)^{-\frac{1}{2}}x;q^{-\frac{1}{2}},q^{-\frac{1}{2}},1,1;q\right).}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle T_{n}}}}$ : Cigler ${\displaystyle{\displaystyle{\displaystyle q}}}$-Chebyshev polynomial ${\displaystyle{\displaystyle{\displaystyle T}}}$ : http://drmf.wmflabs.org/wiki/Definition:CiglerqChebyT
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial with four parameters : http://drmf.wmflabs.org/wiki/Definition:bigqJacobiIVparam

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