Definition:CiglerqChebyT

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The LaTeX DLMF and DRMF macro \CiglerqChebyT represents the Cigler q π‘ž {\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 T n Cigler-q-Chebyshev-polynomial-T 𝑛 {\displaystyle{\displaystyle{\displaystyle T_{n}}}}
\CiglerqChebyT{n}@{x}{s}{q} produces T n ⁑ ( x , s , q ) Cigler-q-Chebyshev-polynomial-T 𝑛 π‘₯ 𝑠 π‘ž {\displaystyle{\displaystyle{\displaystyle T_{n}\!\left(x,s,q\right)}}}

These are defined by T n ⁑ ( x , s , q ) := ( - s ) 1 2 ⁒ n ⁒ P n ⁑ ( ( - q ⁒ s ) - 1 2 ⁒ x ; q - 1 2 , q - 1 2 , 1 , 1 ; q ) . assign Cigler-q-Chebyshev-polynomial-T 𝑛 π‘₯ 𝑠 π‘ž superscript 𝑠 1 2 𝑛 q-Jacobi-polynomial-four-parameters-P 𝑛 superscript π‘ž 𝑠 1 2 π‘₯ superscript π‘ž 1 2 superscript π‘ž 1 2 1 1 π‘ž {\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

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


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