The symbol (the lower case Greek letter tau) has many common uses in mathematics, as summarized in the following table.

1. is an alternate notation for the divisor function .

2. is the half-period ratio of an elliptic function.

3. denotes the tau function of Ramanujan, defined by the generating function

4. is used as an alternate notation for the golden ratio .

5. As a characteristic time for exponential decay or growth, i.e., .

The symbol also has a number of other different meanings in physics, for example the tau particle, tau neutrino, as a symbol for torque, etc.