NOTICE: Citizendium is still being set up on its newer server, treat as a beta for now; please see here for more. |

Citizendium - a community developing a quality comprehensive compendium of knowledge, online and free. Click here to join and contribute—free |

CZ thanks our previous donors. Donate here. Treasurer's Financial Report -- Thanks to our content contributors. -- |

# Theta function

From Citizendium, the Citizens' Compendium

Revision as of 09:13, 3 January 2009 by Richard Pinch (Talk | contribs) (added Jacobi's triple product identity)

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.