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http://functions.wolfram.com/01.22.04.0004.01
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Coth[z + m I Pi] == Coth[z] /; Element[m, Integers]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Coth", "[", RowBox[List["z", "+", RowBox[List["m", " ", "\[ImaginaryI]", " ", "\[Pi]"]]]], "]"]], "\[Equal]", RowBox[List["Coth", "[", "z", "]"]]]], "/;", RowBox[List["m", "\[Element]", "Integers"]]]]]]
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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> coth </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> coth </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> m </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <coth /> <apply> <plus /> <ci> z </ci> <apply> <times /> <pi /> <imaginaryi /> <ci> m </ci> </apply> </apply> </apply> <apply> <coth /> <ci> z </ci> </apply> </apply> <apply> <in /> <ci> m </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", RowBox[List["z_", "+", RowBox[List["m_", " ", "\[ImaginaryI]", " ", "\[Pi]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Coth", "[", "z", "]"]], "/;", RowBox[List["m", "\[Element]", "Integers"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
