In mathematics, the q-theta function (or modified Jacobi theta function) is a type of q-series which is used to define elliptic hypergeometric series.[1] [2] It is given by
| infty | |
| \theta(z;q):=\prod | |
| n=0 |
(1-qnz)\left(1-qn+1/z\right)
where one takes 0 ≤ |q| < 1. It obeys the identities
| \theta(z;q)=\theta\left( | q | ;q\right)=-z\theta\left( |
| z |
| 1 | |
| z |
;q\right).
It may also be expressed as:
\theta(z;q)=(z;q)infty(q/z;q)infty
where
( ⋅ ⋅ )infty