Basic hypergeometric series psi
From specialfunctionswiki
The bilateral basic hypergeometric series $\psi$ is defined by $${}_j\psi_{\ell}(a_1,\ldots,a_j;b_1,\ldots,b_k;q,z)=\displaystyle\sum_{k=-\infty}^{\infty} \dfrac{(a_1;q)_k\ldots(a_j;q)_k}{(b_1;q)_k\ldots(b_{\ell};q)_k}\left( (-1)^k q^{ {k \choose 2} } \right)^{\ell-j}z^k.$$
