The tag has no usage guidance.

learn more… | top users | synonyms

4
votes
0answers
82 views

notation for $(a-b)(a-qb)\dots (a-q^{n-1}b)$

I wonder whether there is a notation for such thing, which I denote $[a;b]_q^n$ for a moment: $$ [a;b]_q^n:=(a-b)(a-qb)\dots (a-q^{n-1}b)=a^n(b/a;q)_n, $$ this last equation uses $q$-Pochhammer symbol ...
4
votes
0answers
73 views

Identities for ${~}_3\phi_1$?

I am looking for some source of summation formulas for the $q$-hypergeometric function ${~}_3\phi_1$ in the sense of Gasper-Rahman book. For some reason, the book focuses heavily on ${~}_{r+1}\phi_r$ ...
1
vote
0answers
220 views

references for q-series identities

I need references for $\sum_{n=0}^N\frac{q^n}{(q^2;q^2)_n(q^2;q^2)_{N-n}}=\frac{(-q,q)_N}{(q^2;q^2)_N}$ and $\sum_{n=0}^N\frac{(-1)^nq^{n^2}}{(q^2;q^2)_n(q;q)_{N-n}}=\frac1{(q^2;q^2)_N}$ A ...