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Let RX = 2+2+x, Rk+1 = V2 + Rk. Then 2k /2-Rk I and 2k 1 6 2 \3 + 3Rk 11/2 both converge to arecos x if x I ? 1 and to arecosh x if 1 < x < oo. Truncation errors for the two expressions are of the order of 2-2k and 2-4k respectively.

Iterated square root expansions for the inverse cosine and inverse hyperbolic cosine