Half-range Fourier series for functions defined over range L

A half-range cosine series in the range 0 to L can be expanded as:(1) f ( x ) = a 0 + ∑ n = 1 ∞ a n c o s ( n π x L ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq6044.tif"/>