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http://functions.wolfram.com/01.26.27.1637.01
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ArcCosh[(1 - z)/(1 + z)] == (1 - Sqrt[1 + z] Sqrt[1/(1 + z)]) Pi I +
2 ArcTanh[Sqrt[-z]]
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Cell[BoxData[RowBox[List[RowBox[List["ArcCosh", "[", FractionBox[RowBox[List["1", "-", "z"]], RowBox[List["1", "+", "z"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List[SqrtBox[RowBox[List["1", "+", "z"]]], SqrtBox[FractionBox["1", RowBox[List["1", "+", "z"]]]]]]]], ")"]], "\[Pi]", " ", "\[ImaginaryI]"]], "+", RowBox[List["2", RowBox[List["ArcTanh", "[", SqrtBox[RowBox[List["-", "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> <mrow> <msup> <mi> cosh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> z </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mfrac> <mn> 1 </mn> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> z </mi> </mrow> </mfrac> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arccosh /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <pi /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <arctanh /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", FractionBox[RowBox[List["1", "-", "z_"]], RowBox[List["1", "+", "z_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List[SqrtBox[RowBox[List["1", "+", "z"]]], " ", SqrtBox[FractionBox["1", RowBox[List["1", "+", "z"]]]]]]]], ")"]], " ", "\[Pi]", " ", "\[ImaginaryI]"]], "+", RowBox[List["2", " ", RowBox[List["ArcTanh", "[", SqrtBox[RowBox[List["-", "z"]]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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