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 Cosh

 http://functions.wolfram.com/01.20.27.0038.01

 Input Form

 a Cosh[z] + b Sinh[z] == Sqrt[1 - b^2/a^2] a Cosh[z + ArcTanh[b/a]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["a", " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], "\[Equal]", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox[SuperscriptBox["b", "2"], SuperscriptBox["a", "2"]]]]], " ", "a", " ", RowBox[List["Cosh", "[", RowBox[List["z", "+", RowBox[List["ArcTanh", "[", FractionBox["b", "a"], "]"]]]], "]"]]]]]]]]

 MathML Form

 a cosh ( z ) + b sinh ( z ) 1 - b 2 a 2 a cosh ( z + tanh - 1 ( b a ) ) a z b z 1 -1 b 2 a 2 -1 1 2 a z b a -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["a_", " ", RowBox[List["Cosh", "[", "z_", "]"]]]], "+", RowBox[List["b_", " ", RowBox[List["Sinh", "[", "z_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox[SuperscriptBox["b", "2"], SuperscriptBox["a", "2"]]]]], " ", "a", " ", RowBox[List["Cosh", "[", RowBox[List["z", "+", RowBox[List["ArcTanh", "[", FractionBox["b", "a"], "]"]]]], "]"]]]]]]]]

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

 2001-10-29