# Specific laplace transform

1. Jan 27, 2009

### TheFerruccio

There are lots of tables out there for finding the inverse laplace transform of:

$$\frac{1}{(s+b)^{2}+a^{2}}$$

or

$$\frac{s}{(s+b)^{2}+a^{2}}$$

but what if $$a^{2}$$ is negative?

I don't know what useful formula I should split it up into.

2. Jan 27, 2009

### matematikawan

If a2 is negative then you may further factored the denominator. Then you formed a partial fraction for the whole expression.

e.g. let a2=-c2.

(s+b)2+a2=(s+b+c)(s+b-c)