Formula:6653

Digital Library of Mathematical Functions ID 18.27.E6

${\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}\left(x;c,d;q\right)=\frac{c^{n}q^{-(\alpha+1)n}\left(q^{\alpha+1},-q^{\alpha+1}c^{-1}d;q\right)_{n}}{\left(q,-q;q\right)_{n}}\*P_{n}\left(q^{\alpha+1}c^{-1}x;q^{\alpha},q^{\beta},-q^{\alpha}c^{-1}d;q\right).}}$

Symbols List

• ${\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}$:
• ${\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},\NVar{c};\NVar{q}\right)}}$: big $$q$$ -Jacobi polynomial
• ${\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle q}}$: real variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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