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http://functions.wolfram.com/01.29.27.0885.01
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ArcCsch[z] == -((Pi I)/2) + ((2 I Sqrt[-z])/Sqrt[I - z]) Sqrt[(z - I)/z]
ArcCsc[Sqrt[-2 z]/Sqrt[I - z]]
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Cell[BoxData[RowBox[List[RowBox[List["ArcCsch", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]], "+", RowBox[List[FractionBox[RowBox[List["2", "\[ImaginaryI]", SqrtBox[RowBox[List["-", "z"]]]]], SqrtBox[RowBox[List["\[ImaginaryI]", "-", "z"]]]], SqrtBox[FractionBox[RowBox[List["z", "-", "\[ImaginaryI]"]], "z"]], " ", RowBox[List["ArcCsc", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "2"]], "z"]]], SqrtBox[RowBox[List["\[ImaginaryI]", "-", "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> csch </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> <msqrt> <mrow> <mi> ⅈ </mi> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mfrac> <mo> ⁢ </mo> <msqrt> <mfrac> <mrow> <mi> z </mi> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mi> z </mi> </mfrac> </msqrt> <mo> ⁢ </mo> <mrow> <msup> <mi> csc </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <msqrt> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msqrt> <msqrt> <mrow> <mi> ⅈ </mi> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arccsch /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <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 /> <imaginaryi /> <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> <power /> <apply> <times /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <arccsc /> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <imaginaryi /> <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> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsch", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", "z"]]]]], ")"]], " ", SqrtBox[FractionBox[RowBox[List["z", "-", "\[ImaginaryI]"]], "z"]], " ", RowBox[List["ArcCsc", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "2"]], " ", "z"]]], SqrtBox[RowBox[List["\[ImaginaryI]", "-", "z"]]]], "]"]]]], SqrtBox[RowBox[List["\[ImaginaryI]", "-", "z"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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