George Castillo added the comment: Just a quick addition here regarding the singularities to these functions. The atanh(x) is only defined for |x| < 1, so atanh(1) or atanh(-1) isn't singular there so much as simply isn't defined. So, even though the function approaches infinite as x -> 1, it wouldn't really be correct to return a value at |x| = 1. I think raising an exception at those points would be more correct.
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