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http://functions.wolfram.com/01.23.06.0023.01
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Csch[z] \[Proportional] Csch[Subscript[z, 0]] - Coth[Subscript[z, 0]]
Csch[Subscript[z, 0]] (z - Subscript[z, 0]) +
3 Csch[Subscript[z, 0]] (-(1/2) + (1/3) Cosh[2 Subscript[z, 0]]
Csch[Subscript[z, 0]]^2) (z - Subscript[z, 0])^2 + \[Ellipsis] /;
(z -> Subscript[z, 0])
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Csch", "[", "z", "]"]], "\[Proportional]", RowBox[List[RowBox[List["Csch", "[", SubscriptBox["z", "0"], "]"]], "-", RowBox[List[RowBox[List["Coth", "[", SubscriptBox["z", "0"], "]"]], " ", RowBox[List["Csch", "[", SubscriptBox["z", "0"], "]"]], " ", RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]]]], "+", RowBox[List["3", " ", RowBox[List["Csch", "[", SubscriptBox["z", "0"], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", SubscriptBox["z", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["Csch", "[", SubscriptBox["z", "0"], "]"]], "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "2"]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", SubscriptBox["z", "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> <mi> csch </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mrow> <mi> csch </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> coth </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> csch </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mrow> <mi> csch </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> csch </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 2 </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> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </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> <csch /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> coth </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <csch /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <csch /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <csch /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <ci> … </ci> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </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["Csch", "[", SubscriptBox["zz", "0"], "]"]], "-", RowBox[List[RowBox[List["Coth", "[", SubscriptBox["zz", "0"], "]"]], " ", RowBox[List["Csch", "[", SubscriptBox["zz", "0"], "]"]], " ", RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]]]], "+", RowBox[List["3", " ", RowBox[List["Csch", "[", SubscriptBox["zz", "0"], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", SubscriptBox["zz", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["Csch", "[", SubscriptBox["zz", "0"], "]"]], "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "2"]]], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", SubscriptBox["zz", "0"]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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