Convergence acceleration of limit periodic continued fractions under asymptotic side conditions

Summary We present a method of convergence acceleration for limitk-periodic continued fractionsK(a_n/1) orK(1/b_n) satisfying certain asymptotic side conditions. The method represents an improvement of the fixed point modification considered by Thron and Waadeland [8], under these conditions. The regularC-fraction expansions of hypergeometric functions₂F₁(a, 1;c; z) and₂F₁(a, b; c; z)/₂F₁(a, b+1;c+1;z) are examples of continued fractions satisfying these conditions.