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: 10px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 ArcCosh

 http://functions.wolfram.com/01.26.06.0032.02

 Input Form

 ArcCosh[z] \[Proportional] (Sqrt[z - 1]/Sqrt[1 - z]) (Pi - Sqrt[2] Sqrt[z + 1] (1 + O[z + 1]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List[SqrtBox[RowBox[List["z", "-", "1"]]], " "]], SqrtBox[RowBox[List["1", "-", "z"]]]], RowBox[List["(", RowBox[List["\[Pi]", "-", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["z", "+", "1"]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "+", "1"]], "]"]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 cosh - 1 ( z ) z - 1 1 - z ( π - 2 z + 1 ( 1 + O ( z + 1 ) ) ) Proportional z z -1 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 1 2 1 O z 1 [/itex]

 Rule Form

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

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

 2001-10-29