We list common periodic functions. In the parentheses, there are given their period with least
modulus.
- One-periodic functions with a real period:
sine (2π), cosine (2π), tangent (π), cotangent (π), secant (2π), cosecant (2π), and
functions depending on them – especially the triangular-wave function (2π); the
mantissa function x−⌊x⌋ (1).
- One-periodic functions with an imaginary period:
exponential function (2iπ), hyperbolic sine (2iπ), hyperbolic cosine (2iπ), hyperbolic
tangent (iπ), hyperbolic cotangent (iπ), and functions depending on them.
- Two-periodic functions: elliptic functions.
- Functions with infinitely many periods:
the Dirichlet’s function
has any rational number as its period; a constant function has any number as its
period.
