## Partial fraction decomposition with complex function

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.
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 Quote by 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.
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

 Quote by 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.

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

DonAntonio

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