On a class of generalized Stieltjes continued fractions - Kovalyov, I.; Derkach, V. A. (Methods of Functional Analysis and Topology, 2015)
With each sequence of real numbers s={s_j}_j=0^∞ two kinds of continued fractions are associated, - the so-called P-fraction and a generalized Stieltjes fraction that, in the case when s={s_j}_j=0^∞ is a sequence of moments of a probability measure on R_+, coincide with the J-fraction and the Stieltjes fraction, respectively. A subclass H^reg of regular sequences is specified for which explicit formulas connecting these two continued fractions are found. For sH^reg the Darboux transformation of the corresponding generalized Jacobi matrix is calculated in terms of the generalized Stieltjes fraction.