Rational Approximation to a Class of Continued Fractions

Abstract:

      Let $f(n)$ be a nonnegative function, and $\kappa,b,s_{i}$ and $t_{i}(i=1,2,\cdots)$ positive constants. We discuss the lower bound of rational approximations to two kinds of continued fractions such as $$[a_{0},a_{1},a_{2},\cdots]=[\overline{\kappa n+b}]_{n=0}^{\infty}\mbox{~~and~~}[\overline{s_{n},f(n),t_{n}}]_{n=1}^{\infty}.$$