Formula:KLS:14.05:54

<< Formula:KLS:14.05:53

formula in Big q-Jacobi

Formula:KLS:14.05:55 >>

${\displaystyle{\displaystyle{\displaystyle U_{n}\!\left(x,q,b\right)=(q^{-3}b)^{\frac{1}{2}n}\frac{1-q^{n+1}}{1-q}P_{n}\!\left(b^{-\frac{1}{2}}x;q^{\frac{1}{2}},q^{\frac{1}{2}},1,1;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle U_{n}}}}$ : Cigler ${\displaystyle{\displaystyle{\displaystyle q}}}$-Chebyshev polynomial ${\displaystyle{\displaystyle{\displaystyle U}}}$ : http://drmf.wmflabs.org/wiki/Definition:CiglerqChebyU
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : 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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