Formula:KLS:14.05:49

<< Formula:KLS:14.05:48

formula in Big q-Jacobi

Formula:KLS:14.05:50 >>

${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(-d;a,b,c,d;q\right)=q^{\frac{1}{2}n(n+1)}(-a)^{n}\frac{\left(qb;q\right)_{n}}{\left(qa;q\right)_{n}}}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial with four parameters : http://drmf.wmflabs.org/wiki/Definition:bigqJacobiIVparam
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.5 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:14.05:48

formula in Big q-Jacobi

Formula:KLS:14.05:50 >>