Tau is the lower case Greek letter 
, which has many uses in mathematics,
as summarized in the following list.
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. 
is an alternate notation for twice
pi.
6. 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.
