Inverse hyperbolic sine: Specific values (formula 01.25.03.0029)

ArcSinh

$Mathematica Notation$

http://functions.wolfram.com/01.25.03.0029.01

Input Form

ArcSinh[-Infinity] == DirectedInfinity[Complex[0, -1]]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["ArcSinh", "[", RowBox[List["-", "\[Infinity]"]], "]"]], "\[Equal]", InterpretationBox[RowBox[List["-", "\[Infinity]"]], DirectedInfinity[Complex[0, -1]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> sinh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <semantics> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> DirectedInfinity </ci> <cn type='complex-cartesian'> 0 <sep /> -1 </cn> </apply> </annotation-xml> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arcsinh /> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> </apply> <apply> <ci> DirectedInfinity </ci> <cn type='complex-cartesian'> 0 <sep /> -1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSinh", "[", RowBox[List["-", "\[Infinity]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["DirectedInfinity", "[", RowBox[List["Complex", "[", RowBox[List["0", ",", RowBox[List["-", "1"]]]], "]"]], "]"]]]]]]

Date Added to functions.wolfram.com (modification date)

2001-10-29