Abstract: The paper considers second
order continued fractions associated with (I) the Psi function (II)
the continued fraction component in due
to Stieltjes. The second order sequences provide
approximants, some of which are remarkably close. In addition, a series form for
the convergent associated
with a continued fraction provides an expression for the derivatives of a
continued fraction. The implementation uses a Maple code for derivatives.
Keywords and phrases: polygamma functions, second order continued fractions, Stieltjes integral.
