Rational approximation of Heaviside function

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hilbert2
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Hi, could someone please help me with this one: I'd need to form a sequence of rational functions ##R_{n}(x)## such that ##\lim_{n \to \infty} R_{n}(x)=\theta(x)##, where ##\theta(x)## is the Heaviside step function. The functions ##R_{n}(x)## should preferably be limited in range, i.e. for some real number ##M##, ##|R_{n}(x)|<M## for all ##n## and ##x##. This is not a homework problem, I just happen to need a rational approximation for the step function.
 

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pwsnafu
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The problem is that rational functions can only have one horizontal asymptote, but Heaviside has two. So you need to be more specific by what you want.
 
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hilbert2
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Ok, thanks for the answer. I was looking for a step function approximation for which the inverse Laplace transform can be calculated in closed form. I probably have to approach the problem some other way.
 

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