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...s of the transforms, are [[complex number|complex]] [[exponential function|exponentials]]. This is, if the input to a system is the complex waveform <math>A_s e^{ Since [[sine wave|sinusoids]] are a sum of complex exponentials with complex-conjugate frequencies, if the input to the system is a sinusoi ...

This representation using complex exponentials may be justified by noting that (by [[Euler's formula]]): These two relationships hold even after taking the real part of the complex exponentials (see [[phasor]]s), which is the part of the signal one actually measures in ...

...Delta A \ll 1</math>, this expression can be approximated by expanding the exponentials in a [[Taylor series]] to first-order and then discarding terms of <math> \ ...

...CFE equations may have a different power of ''F'' (or ''V'') in their pre-exponentials. Measurements of ''κ'' might provide some experimental indication of this. ...ve rise to significantly different expressions for the current-density pre-exponentials, for different classes of material. In particular, the power of barrier fie ...

Later, [[Augustin Cauchy]] expressed the theorem using exponentials:<ref name= Myint-U>{{cite book |first1=Tyn |last1=Myint-U. |first2=Lokenath ...