For the limit periodic /-fraction K(-an/(k + bn)), an , bn £ C , n £ N , which is normalized such that it converges and represents a meromorphic function f(k) on C* :=C\[-1, 1 ], the numerators A" and denominators Bn of its nth approximant are explicitly determined for all n £ N. Under natural conditions on the speed of convergence of an , bn , n-> oo , the asymptotic behaviour of the orthogonal polynomials B" , A"+x (of first and second kind) is investigated on C* and [-1, 1]. An explicit representation for f(X) yields continuous extension of / from C* onto upper and lower boundary of the cut (-1, 1). Using this and a determinant relation, which asymptotically connects both sequences A", B" , one obtains nontrivial explicit formulas for the absolutely continuous part (weight function) of the distribution functions for the orthogonal polynomial sequences Bn , An+X , n £ N. This leads to short proofs of results which generalize and supplement results obtained by P. G. Nevai [7]. Under a stronger condition the explicit representation for f(k) yields meromorphic extension of / from C* across (-1, 1) onto a region of a second copy of C which there is bounded by an ellipse, whose focal points ± 1 are first order algebraic branch points for /. Then, by substitution, analogous results on continuous and meromorphic extension are obtained for limit periodic continued fractions K(-a"(z)/(X(z) + b"(z))) , where an(z), b"(z), \{z) are holomorphic on a region in C. Finally, for /-fractions T(z) = K(-cnz/(\ + dnz)) with cn-> c, dn-» d, n-> oo , the exact convergence regions are determined for all c, d £ C. Again, explicit representations for T(z) yield continuous and meromorphic extension results. For all c, d £ C the regions (on Riemann surfaces) onto which T(z) can be extended meromorphically, are described explicitly.
