# Theta function

From Citizendium, the Citizens' Compendium

In mathematics, a **theta function** is an analytic function which satisfies a particular kind of functional equation. Theta functions occur as generating functions associated to quadratic forms. They are modular forms of half-integer weight.

Jacobi's theta function is a power series in (traditionally referred to as the *nome*)

Jacobi's triple product identity

## References

- Tom M. Apostol (1976).
*Introduction to Analytic Number Theory*. Springer-Verlag. ISBN 0-387-90163-9. - Tom M. Apostol (1990).
*Modular functions and Dirichlet Series in Number Theory*, 2nd ed. Springer-Verlag. ISBN 0-387-97127-0.