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http://functions.wolfram.com/01.03.26.0100.01
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E^(n z) == ChebyshevT[n, Cosh[z]] + ChebyshevU[n - 1, Cosh[z]] Sinh[z]
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Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["n", " ", "z"]]], "\[Equal]", RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", RowBox[List["Cosh", "[", "z", "]"]]]], "]"]], "+", RowBox[List[RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", RowBox[List["Cosh", "[", "z", "]"]]]], "]"]], " ", RowBox[List["Sinh", "[", "z", "]"]]]]]]]]]]
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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> <msup> <mi> ⅇ </mi> <mrow> <mi> n </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⩵ </mo> <mrow> <mrow> <msub> <mi> T </mi> <mi> n </mi> </msub> <mo> ( </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> U </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> n </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <ci> ChebyshevT </ci> <ci> n </ci> <apply> <cosh /> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <sinh /> <ci> z </ci> </apply> <apply> <ci> ChebyshevU </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <apply> <cosh /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", RowBox[List["n_", " ", "z_"]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", RowBox[List["Cosh", "[", "z", "]"]]]], "]"]], "+", RowBox[List[RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", RowBox[List["Cosh", "[", "z", "]"]]]], "]"]], " ", RowBox[List["Sinh", "[", "z", "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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