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 Exp

 http://functions.wolfram.com/01.03.27.0014.01

 Input Form

 a E^z + b/E^z == (a + b) Cosh[z] + (a - b) Sinh[z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["a", " ", SuperscriptBox["\[ExponentialE]", "z"]]], "+", RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]]]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["Sinh", "[", "z", "]"]]]]]]]]]]

 MathML Form

 a z + b - z ( a + b ) cosh ( z ) + ( a - b ) sinh ( z ) a z b -1 z a b z a -1 b z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["a_", " ", SuperscriptBox["\[ExponentialE]", "z_"]]], "+", RowBox[List["b_", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z_"]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["Sinh", "[", "z", "]"]]]]]]]]]]

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

 2001-10-29