If a function is defined over half the range, say 
, instead of the full range from 
, it may be expanded in a series of sine terms only or of cosine terms only. The series produced is then called a half range Fourier series.
Conversely, the Fourier Series of an even or odd function can be analysed using the half range definition.
Even Function and Half Range Cosine Series
An even function can be expanded using half its range from
That is, the range of integration is L. The Fourier series of the half range even function is given by:
