Complex analysis | Types of functions
Quasiperiodic function
In mathematics, a quasiperiodic function is a function that has a certain similarity to a periodic function. A function is quasiperiodic with quasiperiod if , where is a "simpler" function than . What it means to be "simpler" is vague. A simple case (sometimes called arithmetic quasiperiodic) is if the function obeys the equation: Another case (sometimes called geometric quasiperiodic) is if the function obeys the equation: An example of this is the Jacobi theta function, where shows that for fixed it has quasiperiod ; it also is periodic with period one. Another example is provided by the Weierstrass sigma function, which is quasiperiodic in two independent quasiperiods, the periods of the corresponding Weierstrass ℘ function. Functions with an additive functional equation are also called quasiperiodic. An example of this is the Weierstrass zeta function, where for a z-independent η when ω is a period of the corresponding Weierstrass ℘ function. In the special case where we say f is periodic with period ω in the period lattice . (Wikipedia).
