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http://functions.wolfram.com/01.25.27.1627.01
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ArcSinh[Sqrt[-z]/Sqrt[z - 1]] == -ArcCoth[Sqrt[1/z]] /; Im[z] != 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSinh", "[", FractionBox[SqrtBox[RowBox[List["-", "z"]]], SqrtBox[RowBox[List["z", "-", "1"]]]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List["ArcCoth", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[NotEqual]", "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> <mrow> <msup> <mi> sinh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <msqrt> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mrow> <msup> <mi> coth </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ≠ </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arcsinh /> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arccoth /> <apply> <power /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <neq /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSinh", "[", FractionBox[SqrtBox[RowBox[List["-", "z_"]]], SqrtBox[RowBox[List["z_", "-", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List["ArcCoth", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[NotEqual]", "0"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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