An almost periodic function
13 hours ago
- The post generalizes the previous question about sine in radians vs degrees by considering any two positive numbers with an irrational ratio.
- The function f(x) = sin(αx) − sin(βx) is almost periodic, meaning it is not periodic but can be arbitrarily close to periodic over long intervals.
- f(x) is the product of two periodic functions but is not periodic itself because the ratio of their frequencies is irrational.
- The zeros of f are not periodic, but they can be divided into two periodic subsequences.