Singularities[Sinh[z], z] == {{ComplexInfinity, Infinity}}

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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> <msub> <mi> &#119982;&#119998;&#120003;&#8458; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mo> { </mo> <mrow> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#119982;&#119998;&#120003;&#8458; </ci> <ci> z </ci> </apply> <apply> <sinh /> <ci> z </ci> </apply> </apply> <list> <list> <apply> <ci> OverTilde </ci> <infinity /> </apply> <infinity /> </list> </list> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Singularities", "[", RowBox[List[RowBox[List["Sinh", "[", "z_", "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]], "}"]]]]]]

2001-10-29