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