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http://functions.wolfram.com/01.20.16.0104.01
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(Cosh[z] - Sinh[z])^n == Cosh[n z] - Sinh[n z] /;
Element[n, Integers] && n >= 0
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Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", "z", "]"]], "-", RowBox[List["Sinh", "[", "z", "]"]]]], ")"]], "n"], "\[Equal]", RowBox[List[RowBox[List["Cosh", "[", RowBox[List["n", " ", "z"]], "]"]], "-", RowBox[List["Sinh", "[", RowBox[List["n", " ", "z"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["n", ",", "Integers"]], "]"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> ⩵ </mo> <mrow> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <mi> ℕ </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <plus /> <apply> <cosh /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sinh /> <ci> z </ci> </apply> </apply> </apply> <ci> n </ci> </apply> <apply> <plus /> <apply> <cosh /> <apply> <times /> <ci> n </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sinh /> <apply> <times /> <ci> n </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> ℕ </ci> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", "z_", "]"]], "-", RowBox[List["Sinh", "[", "z_", "]"]]]], ")"]], "n_"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Cosh", "[", RowBox[List["n", " ", "z"]], "]"]], "-", RowBox[List["Sinh", "[", RowBox[List["n", " ", "z"]], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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