Q贝塞尔多项式

qBessel function 2D plot

q-贝塞尔多项式，也称q-贝塞尔函数，其通过基本超几何函数定义：

$y_n(x;a;q)={}_2{\varphi }_1(\begin{array}{cc}{q}^{-N}& -a{q}^n\\ 0\end{array};q,qx)$

正交关系

$\sum _{k=0}^{\mathrm{\infty }}(\frac{a^k}{(q;q{)}_n}*q^{(\genfrac{}{}{0ex}{}{k+1}{2})}*y_m*(q^k;a;q)*y_n*(q^k;a;q)=(q;q{)}_n*(-a{q}^n;q{)}_{\mathrm{\infty }}\frac{a^n*q^{(\genfrac{}{}{0ex}{}{n+1}{2})}}{1+a{q}^{2n}}{\delta }_{mn}$

图集

QBessel function abs complex 3D Maple plot

QBessel function Im complex 3D Maple plot

QBessel function Re complex 3D Maple plot

QBessel function abs density Maple plot

QBessel function Im density Maple plot

QBessel function Re density Maple plot

参考文献

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