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 Cosh

 http://functions.wolfram.com/01.20.27.0014.01

 Input Form

 Cosh[z] == 1/Sqrt[1 + Tan[I z]^2] /; Abs[Im[z]] < Pi/2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Cosh", "[", "z", "]"]], "\[Equal]", FractionBox["1", SqrtBox[RowBox[List["1", "+", SuperscriptBox[RowBox[List["Tan", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]], "2"]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], "<", FractionBox["\[Pi]", "2"]]]]]]]

 MathML Form

 cosh ( z ) 1 1 + tan 2 ( z ) /; "\[LeftBracketingBar]" Im ( z ) "\[RightBracketingBar]" < π 2 Condition z 1 1 z 2 1 2 -1 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["1", "+", SuperscriptBox[RowBox[List["Tan", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]], "2"]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], "<", FractionBox["\[Pi]", "2"]]]]]]]]]

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

 2001-10-29