21. Conversely every such series is the expansion of some Besicovitch periodic function ( which is not unique ). 22. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. 23. Then the periodic function represented by the Fourier series is a periodic summation of X ( f ). 24. The characteristic wave patterns of periodic functions are useful for modeling recurring phenomena such as sound or light waves. 25. The totality of meromorphic doubly periodic functions with given periods defines an algebraic function field associated to that curve. 26. However, F is a continuous periodic function , so by the previous special case F is uniformly zero. 27. VeG vroha has been studied from a modern perspective and the process is explained using the properties of periodic functions . 28. In other words, if you multiply a plane wave by a periodic function , you get a Bloch wave. 29. Periodic functions ( such as \ sin ( t ) ) are particularly well-suited for this sub-division.30. The notion of quasi-periodic functions was generalised still further by Harald Bohr when he introduced almost-periodic functions.
