On Stieltjes’ continued fraction for the gamma function

Stieltjes continued fraction and QD algorithm; scalar, vector, matrix cases.

Asymptotic Behavior of the Continued Fraction Coefficients of a Class of Stieltjes Transforms including the Binet Function

Continued-fraction Expansions for the Riemann Zeta Function and Polylogarithms

It appears that the only known representations for the Riemann zeta function ζ(z) in terms of continued fractions are those for z = 2 and 3. Here we give a rapidly converging continued-fraction expansion of ζ(n) for any integer n ≥ 2. This is a special case of a more general expansion which we have derived for the polylogarithms of order n, n ≥ 1, by using the classical Stieltjes technique. Our...

Convergence Conditions for Vector Stieltjes Continued Fractions

Necessary and sufficient conditions for the convergence of vector S-fractions are obtained, generalizing classical results of Stieltjes. A class of unbounded difference operators of high order possessing a set of spectral measures is described.

A CONTINUED FRACTION EXPANSION FOR A q-TANGENT FUNCTION

We prove a continued fraction expansion for a certain q–tangent function that was conjectured by Prodinger.