A periodic function 
is a function with a nonzero period 
satisfying
 |
for 
,
2, .... A singly periodic function has
one independent period. For example, the sine
function 
,
illustrated above, is periodic with least period
(often simply called "the" period) 
(as well as with period 
, 
, 
, etc.).
The constant function 
is periodic with any period 
for all nonzero real numbers 
, so there is no least period
for constant functions. The following table
summarizes the names given to periodic functions based on the number of independent
periods they possess.
| number of periods | name |
| 1 | singly periodic function |
| 2 | doubly periodic function |
| 3 | triply periodic function |
