In mathematics, the q-Bessel polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.
The polynomials are given in terms of basic hypergeometric functions by [1] ：
yn(x;a;q)= {}2\phi1\left(\begin{matrix}q-n&-aqn\ 0\end{matrix};q,qx\right).
K(x;a;q).
| infty | ||
| \sum | \left( | |
| k=0 |
| ak | |
| (q;q)n |
*qk+1*ym
| k;a;q)*y | |
| *(q | |
| n |
| k;a;q)\right)=(q;q) | |
| *(q | |
| n |
| n;q) | |
| *(-aq | |
| infty |
| an*qn+1 | |
| 1+aq2n |
\deltamn
| n;q) | |
| (q;q) | |
| infty |