Continued fractions and functions

[tpm]

for any function $$f(x)$$ how can you convert it to continued fractions in the form:

$$\frac{a_{0}+a_{1}x+a_{2}x^{2}+...}{b_{0}+b_{1}x+b_{2}x^{2}+...}$$

where we must determine the a(n) and b(n) if $$f(x)=x^{1/2}$$ i know how to do it.

 

[NateTG]

That's not actually what people usually call a continued fraction. For more on continued fractions you could refer to:
http:/mathworld.wolfram.com/ContinuedFraction.html

Functions can't always be expressed in that form.
http://mathworld.wolfram.com/WeierstrassFunction.html

Are you familiar with the Taylor-McLaurin series?