atanh hyperbolic tangent inverse Syntax t = atanh(x) Arguments x a real or complex vector/matrix. t a real or complex vector/matrix. Description The components of vector t are the hyperbolic tangent inverse of the corresponding entries of vector x. Definition domain is [-1,1] for the real function (see Remark). Remark In Scilab (as in some others numerical software) when you try to evaluate an elementary mathematical function outside its definition domain in the real case, then the complex extension is used (with a complex result). The most famous example being the sqrt function (try `sqrt(-1)`!). This approach has some drawbacks when you evaluate the function at a singular point which may lead to different results when the point is considered as real or complex. For atanh(), this occurs for -1 and 1, because at these points the imaginary part does not converge and so atanh(1) = +Inf + i NaN while atanh(1) = +Inf for the real case (as lim x->1 of `atanh(x)`). So when you evaluate this function on the vector [1 2] then like 2 is outside the definition domain, the complex extension is used for all the vector and you get atanh(1) = +Inf + i NaN while you get atanh(1) = +Inf with [1, 0.5] for instance. Examples See also tanh ieee