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What is e? 
The constant e is a transcendental number that can be obtained as:

In general, the exponential function plays an important role in processes where the change of a quantity is related to its magnitude (processes usually described by differential equations).

The value of e:

But better look here:

Importance in crystallography
Periodically varying functions can be expressed either as sines and cosines, or as complex exponentials. eix is periodic, and can be used to describes X-ray waves (or periodic/oscillating physical processes in general).

The Euler's formula:


is the basic relationship between these two representations. If we expand each of the functions above in an infinite series, we can prove that: