Simple and analytically tractable expressions for functional determinants are
known to exist for many cases of interest. We extend the range of situations
for which these hold to cover systems of self-adjoint operators of the
Sturm-Liouville type with arbitrary linear boundary conditions. The results
hold whether or not the operators have negative eigenvalues. The physically
important case of functional determinants of operators with a zero mode, but
where that mode has been extracted, is studied in detail for the same range of
situations as when no zero mode exists. The method of proof uses the properties
of generalised zeta-functions. The general form of the final results are the
same for the entire range of problems considered.Comment: 28 pages, LaTe