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http://functions.wolfram.com/01.23.06.0004.02
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Csch[z] \[Proportional] -I + (I/2) (z - (I Pi)/2)^2 -
((5 I)/24) (z - (I Pi)/2)^4 + \[Ellipsis] /; (z -> (Pi I)/2)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Csch", "[", "z", "]"]], "\[Proportional]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", RowBox[List[FractionBox["\[ImaginaryI]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"]]], ")"]], "2"]]], "-", RowBox[List[FractionBox[RowBox[List["5", "\[ImaginaryI]"]], "24"], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"]]], ")"]], "4"]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "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> <mrow> <mi> csch </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> + </mo> <mrow> <mfrac> <mi> ⅈ </mi> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mn> 24 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mo> … </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <csch /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <times /> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 5 </cn> <imaginaryi /> <apply> <power /> <cn type='integer'> 24 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <ci> … </ci> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Csch", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"]]], ")"]], "2"]]], "-", RowBox[List[FractionBox["1", "24"], " ", RowBox[List["(", RowBox[List["5", " ", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"]]], ")"]], "4"]]], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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