Abstract
We present a method of convergence acceleration for limitk-periodic continued fractionsK(an/1) orK(1/bn) 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.
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