Formula:KLS:14.05:55

<< Formula:KLS:14.05:54

formula in Big q-Jacobi

Formula:KLS:14.05:56 >>

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

Proof

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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

Bibliography

Equation in Section 14.5 of KLS.

URL links

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formula in Big q-Jacobi

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