I'm trying to work something on inverse Laplace transform. I need to express a transfer function F(s) to the form(adsbygoogle = window.adsbygoogle || []).push({});

[tex]F(s)=\frac{s^{-1} (a_0 + a_1s^{-1} + a_2s^{-2}+ ... }{b_0 + b_1s^{-1} + b_2s^{-2}+ ... }[/tex]

I can easily do it for rational function e.g.

[tex]\frac{s^3+2s^2+3s+1}{s+4}= \frac{s^{-1} (1+2s^{-1}+3s^{-2}+s^{-3})}{s^{-3}+4s^{-4}}[/tex]

for some indicial e.g

[tex]\frac{1}{\sqrt{s^2+s}}=\frac{1}{s}(1+s^{-1})^{-1/2}[/tex]

Expand using the binomial theorem.

My problem is how to express irrational functions such as s^{-3/2}or

[tex]\frac{e^{-\sqrt{s}}}{s}[/tex]

to the form of F(s).

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# Series expansion

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