Q-theta function

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

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

where one takes $0\leq |q|<1.$ It obeys the identities

$\theta (z;q)=\theta (q/z;q)=-z\theta (1/z;q).\,$

See also

• Jacobi theta function
• Ramanujan theta function