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.
It is given by
:<math>\theta(z;q):=\prod_{n=0}^\infty (1-q^nz)\left(1-q^{n+1}/z\right)</math>
where one takes 0 ≤ |q| < 1. It obeys the identities
:<math>\theta(z;q)=\theta\left(\frac{q}{z};q\right)=-z\theta\left(\frac{1}{z};q\right). </math>
It may also be expressed as:
:<math>\theta(z;q)=(z;q)_\infty (q/z;q)_\infty</math>
where <math>(\cdot \cdot )_\infty</math> is the q-Pochhammer symbol.
See also
- elliptic hypergeometric series
- Jacobi theta function
- Ramanujan theta function