X-Git-Url: http://gitweb.scilab.org/?p=scilab.git;a=blobdiff_plain;f=scilab%2Fmodules%2Felementary_functions%2Fhelp%2Fen_US%2Ftrigonometry%2Fatanh.xml;h=60dce6fe1fe7e8e3a5f4f36eefcfb212d08ab613;hp=b5f40b40ddc0e0bb7d75d97cb87b97358e43ca59;hb=807fe176da3bcb88ce29ad8401cd97aa22cc1c1f;hpb=025bb6738d47ccbd9093b90bc22b9710c41227c0 diff --git a/scilab/modules/elementary_functions/help/en_US/trigonometry/atanh.xml b/scilab/modules/elementary_functions/help/en_US/trigonometry/atanh.xml index b5f40b4..60dce6f 100644 --- a/scilab/modules/elementary_functions/help/en_US/trigonometry/atanh.xml +++ b/scilab/modules/elementary_functions/help/en_US/trigonometry/atanh.xml @@ -13,7 +13,10 @@ * along with this program. * --> - + atanh hyperbolic tangent inverse @@ -55,20 +58,26 @@ 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 have some drawbacks when you - evaluate the function at a singular point which may led to different - results when the point is considered as real or complex. For the - atanh this occurs for -1 and - 1 because the at these points the imaginary part do not + 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] + 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. + atanh(1) = +Inf + i NaN while you get + atanh(1) = +Inf with [1, 0.5] for instance.