Hi

I have a question a series expansion of the following equation

With the eigenvalues determined from

And are given as:

The factors in the expression are:

Real value:

Complex value:

Complex coordinate:

My question is how the eigenfunction series expansion looks like with the above given and what topics do I need to study on to understand the problem? I guess that you can't use orthogonal eigenfunction expansions like the generalized Fourier series because it is a complex expression and because the eigenfunction aren't orthogonal (as far as I understand). This area is new to me and since I am an not a mathematician but a mechanical engineer I would appreciate very much if you will consider that in your replies

Thanks in advance

Regards Brian