Applications of Series

Most functions can be expanded into infinite series form. This is an advantage in physical applications where one is dealing with very small numbers or a small difference between two functions. In those cases, the first few terms of a series may provide a satisfactory description of a physical phenomenon in a much simpler form than the entire function.

Exponential SeriesTrigonometric FunctionsBinomial ExpansionTaylor Series
Natural Log SeriesFourier Series
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Exponential Series

The exponential can be expanded as an infinite series:

Some applications of exponential series are:

Planck radiation formula at low temperatures:

Einstein specific heat
Spin polarization in NMR
Decay probability
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