Consider the case in which one of the roots is repeated:

The expansion for this case is:

Most of the unknown coefficients can be found using the "cover-up" method.

However if we try to apply the same technique
to find A_{2}, we find that it fails:

If we evaluate this expression at s=-2, then
the first and last terms drop out, but both middle terms survive. In fact
the third term is undefined (a divide by 0 condition). Clearly
we need another technique to find the coefficient A_{2}.

© Copyright 2005 to 2019 Erik Cheever This page may be freely used for educational purposes.

Erik Cheever Department of Engineering Swarthmore College