html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 ArcTanh

 http://functions.wolfram.com/01.27.27.2374.01

 Input Form

 ArcTanh[Sqrt[z]] == -((Pi Sqrt[-z^2])/(2 z)) + Sqrt[z] Sqrt[1/z] ArcCosh[Sqrt[z/(z - 1)]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcTanh", "[", SqrtBox["z"], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]], RowBox[List["2", "z"]]]]], "+", RowBox[List[SqrtBox["z"], SqrtBox[FractionBox["1", "z"]], RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["z", RowBox[List["z", "-", "1"]]]], "]"]]]]]]]]]]

 MathML Form

 tanh - 1 ( z ) z 1 z cosh - 1 ( z z - 1 ) - π - z 2 2 z z 1 2 z 1 2 1 z -1 1 2 z z -1 -1 1 2 -1 -1 z 2 1 2 2 z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", SqrtBox["z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]], RowBox[List["2", " ", "z"]]]]], "+", RowBox[List[SqrtBox["z"], " ", SqrtBox[FractionBox["1", "z"]], " ", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["z", RowBox[List["z", "-", "1"]]]], "]"]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2003-08-21