I was looking into applications of continued fractions in Physics, I found that it is possible to find a rational estimate of an irrational function; which I guess can be used for creating bode plots and any calculations that depend on a transfer function to be rational.
But how is it possible to write a Taylor series expansion as a continued fraction? Say we have a functions,
$$H(s) = \frac{1}{cosh(\sqrt(s))}$$
and we want to write it as a Polynomial/Polynomial, how can we do that using continued fraction of Taylor series?
And secondary question, is there a reason to use continued fractions over just using the Taylor series? would you get a better estimate maybe?