Rational Approximations for Irrational Functions using Collocating Continued Fraction Expansions

This paper is motivated by the need in certain engineering contexts to construct approximations for irrational functions in the complex variable z. The main mathematical tool that will be used is a special continued fraction expansion that cause the rational approximant to collocate the irrational function at specific important values of z. This paper introduces two theorems that facilitate the construction of the rational approxima- tion.