Given a differential equation d⁴w/dx⁴ +λ⁴w=0, under boundary conditions w(±1/2)=0, w' (±1/2)=0, it is known that there exist a set of normalized orthogonal functions Cn(x), Sn(x) which represent solution of eigen-value/function problem. It is also known that any function f(x) which is (together with its derivatives f', f'', f''') are continuous in the region and satisfies the end-conditions f(±1/2)=0, f'(±1/2)=0, can be expanded into Fourier-type infinite series in Cn(x) and Sn(x). In the present note, the author discusses about the similar expansion, for the case in which the given function does not fully satisfy the required condition. It is also pointed out that similar line of thoughts can be applied to linear differential equation of any degree, with any number of independent variables.