连续q雅可比多项式

连续q雅可比多项式定义如下

$P_n^{(\alpha ;\beta )}(x|q)=$$\frac{(q^{\alpha +1};q{)}_n}{(q;q;{)}_n}$

• ${}_4{\mathrm{\Phi }}_3$$(q^{-n},q^{n+\alpha +\beta +1};q^{\alpha /2+1/4}{e}^{i\theta };q^{\alpha /2+1/4}{e}^{-i\theta })$

极限关系

连续q雅可比多项式→连续q拉盖尔多项式

$\underset{\beta \to \mathrm{\infty }}{\lim }{P}_n^{(\alpha ;\beta )}(x|q)=P_n^{(\alpha )}(x|q)$

连续q雅可比多项式→雅科比多项式

$\underset{q\to 1}{\lim }{P}_n^{(\alpha ;\beta )}(x|q)=P_n^{(\alpha ;\beta )}(x|q)$

图集

CONTINUOUS Q-JACOBI ABS COMPLEX 3D MAPLE PLOT

CONTINUOUS Q-JACOBI IM COMPLEX 3D MAPLE PLOT

CONTINUOUS Q-JACOBI RE COMPLEX 3D MAPLE PLOT

CONTINUOUS Q-JACOBI ABS DENSITY MAPLE PLOT

CONTINUOUS Q-JACOBI IM DENSITY MAPLE PLOT

CONTINUOUS Q-JACOBI RE DENSITY MAPLE PLOT

参考文献

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