# Rational approximation of Heaviside function

Gold Member
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.