Formula:KLS:14.10:68

<< Formula:KLS:14.10:67

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:69 >>

${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\alpha)}_{n}\!\left(x|q\right)\lx@stackrel{{\scriptstyle q^{\alpha+\frac{1}{2}}\rightarrow\beta}}{{\longrightarrow}}\frac{\left(\beta q^{\frac{1}{2}};q\right)_{n}}{\left(\beta^{2};q\right)_{n}}\beta^{\frac{1}{2}n}C_{n}\!\left(x;\beta\,|\,q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqJacobi
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle C_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-ultraspherical/Rogers polynomial : http://dlmf.nist.gov/18.28#E13

Bibliography

Equation in Section 14.10 of KLS.

URL links

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<< Formula:KLS:14.10:67

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:69 >>