Formula:KLS:14.05:72

<< Formula:KLS:14.05:71

formula in Big q-Jacobi: Special case

Formula:KLS:14.05:76 >>

${\displaystyle{\displaystyle{\displaystyle q^{-n}(1-q^{n})(1-q^{n+1})x^{2}y(x){}=B(x)y(qx)-\left[B(x)+D(x)\right]y(x)+D(x)y(q^{-1}x)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle D(x)=(x-q)(x-cq)}}}$ &

${\displaystyle{\displaystyle{\displaystyle B(x)=q(x-1)(x-c)}}}$ &

${\displaystyle{\displaystyle{\displaystyle y(x)=P_{n}\!\left(x;c;q\right)}}}$

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

& : logical and
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqLegendre

Bibliography

Equation in Section 14.5 of KLS.

URL links

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

<< Formula:KLS:14.05:71

formula in Big q-Jacobi: Special case

Formula:KLS:14.05:76 >>