q-theta function

In mathematics, the q-theta function is a type of q-series. It is given by

$\theta (z;q)=\prod _{n=0}^{\infty }(1-q^{n}z)\left({\frac {1-q^{n+1}}{z}}\right)$

where one takes 0 ≤ |q| < 1. It obeys the identities

$\theta (z;q)=\theta (q/z;q)=-z\theta \left({\frac {1}{z}};q\right).\,$

See also

• Jacobi theta function
• Ramanujan theta function