Rational approximation of some irrational functions through a flexible continued fraction expansion

A simple method is given for the continued fraction expansion (CFE) of the irrational functions (s
²
+ 1)
^1/2
, (s + 1)
^1/2
, and s
^1/2
with adjustable parameters. Explicit formulas are derived for the coefficients of the rational function obtained by truncating such a CFE. The flexibility offered by the adjustable parameters is illustrated by an example.