# Fourier Series Alternative Forms

Cuthbert Nyack

The general form of the Fourier series is shown below. Because
of the relation between sines and cosines, the series can be represented
as a sum of either sines or cosines.
Normalising the coefficients gives:-
The above expression can be represented by either of the
following alternative forms of the Fourier Series.
The 2 variables a_{n} and b_{n} has been
replaced by c_{n} (c_{n}^{2} =
a_{n}^{2} + b_{n}^{2} ) and q_{n}
or f_{n}.

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COPYRIGHT © 1996 Cuthbert Nyack.