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http://functions.wolfram.com/01.26.27.0012.01
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ArcCosh[z] == -2 I (Sqrt[z - 1]/Sqrt[1 - z])
Log[Sqrt[(z + 1)/2] + I Sqrt[(1 - z)/2]]
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Cell[BoxData[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", FractionBox[RowBox[List[SqrtBox[RowBox[List["z", "-", "1"]]], " "]], SqrtBox[RowBox[List["1", "-", "z"]]]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[FractionBox[RowBox[List["z", "+", "1"]], "2"]], "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[FractionBox[RowBox[List["1", "-", "z"]], "2"]]]]]], "]"]]]]]]]]
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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> <mi> cosh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mfrac> <mrow> <msqrt> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <mtext> </mtext> </mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mfrac> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msqrt> <mfrac> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> </msqrt> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arccosh /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -2 </cn> <imaginaryi /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List["z", "-", "1"]]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[FractionBox[RowBox[List["z", "+", "1"]], "2"]], "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[FractionBox[RowBox[List["1", "-", "z"]], "2"]]]]]], "]"]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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