Partial fraction decomposition with complex function

thayin

As part of a project I have been working on I fin it necessary to manipulate the following expression.

e^(icx)/(x^2 + a^2)^2 for a,c > 0

I would like to decomp it into the form

A/(x^2 + a^2) + B/(x^2 + a^2) = e^(icx)/(x^2 + a^2)^2

but I am having trouble getting a usable outcome.

yus310

You need to apply laplace's transform to this to solve for this. you have the write set up, BUT

A/(x^2+a^2) + B/((x^2+a^2)^2), look up laplace transforms and do it as so... you can solve it then.

Yus310

DonAntonio

No wonder you're having problems: it can't be done, as your function is a transcendental function (i.e., [tex]e^{icx}[/tex] is NOT a polynomial, whereas the sum of fractions you want is a rational function.

DonAntonio